IM Alg2.1.8 Lesson: The nᵗʰ Term
Which one doesn’t belong?
A: [math]5+2+2+2+2+2+2[/math][br]B: [math]5+6\cdot2[/math][br]C: [math]5\cdot2^6[/math][br]D: [math]5\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2[/math]
Clare takes a piece of paper with length 8 inches and width 10 inches and cuts it in half. Then she cuts it in half again, and again. . .
Instead of writing a recursive definition, Clare writes [math]C\left(n\right)=80\cdot\left(\frac{1}{2}\right)^n[/math], where [math]C[/math] is the area, in square inches, of the paper after [math]n[/math] cuts. Explain where the different terms in her expression came from.[br]
Approximately what is the area of the paper after 10 cuts?[br]
Kiran takes a piece of paper with length 8 inches and width 10 inches and cuts away one inch of the width. Then he does it again, and again. . .
Complete the table for the area of Kiran’s paper [math]K(n)[/math], in square inches, after [math]n[/math] cuts.
Kiran says the area after 6 cuts, in square inches, is [math]80-8\cdot6[/math]. Explain where the different terms in his expression came from.[br]
Write a definition for [math]K\left(n\right)[/math] that is not recursive.[br]
[size=150]Which is larger, [math]K(6)[/math] or [math]C(6)[/math]?[/size]
A Sierpinski triangle can be created by starting with an equilateral triangle, breaking the triangle into 4 congruent equilateral triangles, and then removing the middle triangle. Starting from a single black equilateral triangle:
[img]data:image/png;base64,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[/img][br][br]Let [math]S[/math] be the number of black triangles in Step [math]n[/math]. Define [math]S(n)[/math] recursively.
Andre and Lin are asked to write an equation for [math]S[/math] that isn't recursive. Andre writes [math]S\left(n\right)=3^n[/math] for [math]n\ge0[/math] while Lin writes [math]S\left(n\right)=3^{n-1}[/math] for [math]n\ge1[/math]. Whose equation do you think is correct? Explain or show your reasoning.[br]
Here is a geometric sequence.
3, ____, 6, ____, 12, ____, 24[br][br]Find the missing terms.
IM Alg2.1.8 Practice: The nᵗʰ Term
[size=150]A sequence is defined by [math]f\left(0\right)=-20[/math], [math]f\left(n\right)=f\left(n-1\right)-5[/math] for [math]n\ge1[/math].[/size][br][br]Explain why [math]f\left(1\right)=-20-5[/math].
Explain why [math]f\left(3\right)=-20-5-5-5[/math].
Complete the expression: [math]f\left(10\right)=-20-[/math]_____. Explain your reasoning.
[size=150]A sequence is defined by [math]f\left(0\right)=-4,f\left(n\right)-f\left(n-1\right)-2[/math] for [math]n\ge1[/math]. Write a definition for the [math]n^{th}[/math] term of the sequence.[/size]
Here is the recursive definition of a sequence:
[math]f\left(1\right)=3[/math], [math]f\left(n\right)=2\cdot f\left(n-1\right)[/math] for [math]n\ge2[/math].[br][br]Find the first 5 terms of the sequence.[br]
Graph the value of the term as a function of the term number.
Is the sequence arithmetic, geometric, or neither? Explain how you know.[br]
Here is a graph of sequence M.
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATUAAAD8CAYAAAAWjzPMAAAgAElEQVR4Ae2dTazdRhXHww6Vj3bRRVYk3aBQCaVJhUqT0EYVaYhCmqJS1PJV2HUFWWZHBZs0aWkXCAIF8SWR8CVeFl0ggYjURahQBQUJiliAVLFBAjaIHTL6Ofe8Z/vM3GvfZ3vOy/uPNPL12Nce/+fMz2fG4/GeSkEKSAEpcAspsOcWuhZdihSQAlKgEtRkBFJACtxSChSB2l//+tfq+vXr1b///e9bSkxdjBSQAuUV2DbUANNnPvOZas+ePdUXvvCFpVf0s5/9rNq/f3+9L/sTjx8/XgE5BSkgBaTAGApsC2rA6J577tmE1DKo/epXv6r3u/3226sXXnihYv3zn/98nQbo5LWNUZw6hhSQAmtDDa/rjjvuqAxSqzy1Bx98sN6365VxnFX/VTFJASkgBfoqsDbUDh48WBHxsMwLy3lqv/3tb2twPfXUU8l87du3r26WJjcqUQpIASkwQIG1oQbMrMm4Cmo0N/HGvv3tbyezZs1Q4KcgBaSAFNiOAmtDrXnSVVDDgwNq7JcKtp2mqIIUkAJSYDsKzAI188S6/WmW8VVQtP20lAJSQAqsUmAWqPGQAE8tF9aB2rVr16pvfvOb2fjlL3+5euaZZxSlgWxgB9vA5cuXBw/5ypMmR6BE+ioonT17toaa9cF1D7Hq/939Wf/Xv/61ND7yyCPVH/7wh6URz3HquLGxUVnBTH2uVccnHzdu3Jj8mlflgzxE0oQyWpXnObZzE57jPKvOEclmTZMUA3Jps0DN+syAVyqsepCQ+s+yNAoNz5Bl6cCbE9/5zndKZ6M+P/mIoAl5iKQJZRQhUIEjhEg2u2Ohtgp6QwvaIMmydADkkSqwoNa2CMomd7Nt7zn9WhSoRbLZsFCzcWrAKxWszy3XPE39Z1ka4+fw1HjboXSIdNeTp+atAU3kqbV1iWSzYaGGZLkBtngOAIh+tzGCHY9jRmiCRjIQQc1bmKDmNYlks6GhxsBbIMPL7+aRASB7d3SsJoA1PQ1qpZugkQxEUPMVWFDzmkSy2dBQQzobr2bAsWXuTQMv9+oUa3rasUs3QSP1Twhq3n7QZKwbqj/6sBQqcIQQyWaLQQ2Pi/6yPsZB/xr7EvGi+O9Yodv0NLCNeY6heY101xPUfOnJU/OaRLLZYlDzspRJ6TY9DWolm6CRDERQ83YpqHlNItnsrodat+lpUCvZBI3kygtqvgKjSZ8Whv/n+ClqfnpNdzXUck1PA1upJmiku56g5iuNPDWvSSSb3dVQyzU9DWqlmqCRDERQ8xVYUPOaRLLZXQ21XNPToFaqCarmp680eM3AJEIgH2p+tksiks3uWqh1m5579+6tx8Tddddd9dLAVqIJGslA5Km1Ky9rgprXJJLN7iqoMfXQD37wgzp+6lOf2oTXAw88UNlrV3hn99577+a2M2fOVM8++2wdL126VBs0Rj1lfPHFF6sLFy5Meo6++ScfzI7Rd/+p9iMPkTShjKa61iHHpQIP2X+qfSPZ7K6C2t///vfK4t13312D6/HHH6/TPvaxj9XrDz/8cPWb3/ymOn36dL3+7ne/u14njYjnNnVkNt9I0+xo6qF2mVM2lNHUdtDn+FaB++w75T6RbNY08f5kPmWUqYfyh59+C4VL87L5URf7DumTTz65mQG2sx/7zxkiufLc2ee+/pTW5IG8RAjkgzKKEKjAEUIkm92VUOOpZhNoGEUKaqSzX26mkKmMKdKTJEHNlzKaUEYRQhSoRbLZXQu1rkHmoMZ+gtq8nmq3bFiP5qkJau1SEtTaeoRYWwa1uTMYyZWXp+ZLX81Pr0kkm92VnpovknzzM7Xv1GmR7nqCmi9tNT+9JpFsVlBblE8kTy2SgQhqvgILal6TSDYbHmq4tY8++mh1xx131E8i9+/fX3fqj/1ELhLUIrnygpqvwGhCGUUIVOAIIZLNhoaazXzLtN42nxqTRt5+++015JhnbawgqKWVFNS8LoKa10RQ85okU4AXQLOpvG0n+ygLbwGMFSJBLZIrL6h5C0MTyihCiOKpRbLZsJ4aIGPgK55ZKvAyOk3SsUIkqEW66wlq3sLkqXlNItlsWKghG1DLzZSBF3eremqRDERQ8xVYUPOaRLLZ0FCz15S6H1mxdN43GytE8tQiufKCmrcwNFHzs61LJJsNDTWaoDbn2fHjx+t3/1jipXVB15Z4+FokqEW66wlq3pbkqXlNItlsaKiZdDwsoClqcV2gMfXQxsZGMj700EObzd3nnnuuykUMeuoYaRoXTT3kyxtNNPVQW5dINhsaajzlZFwanpl9Hs8Ah8fWfSpqEMwt//KXv1S5+Nhjj9VQ+8AHPlD99Kc/zUbuSFNHoImRTH2ePscnH9wI+uw75T7kIZIm5q1Nec19jk0F7rPf1PuUsFmavKnrCgs1gMXTTYDWHY8G4PDaANtYIVLzM1L/BMY69kDndcpML7SnVaMCRwiRbDYs1OyjKLmmpj0s6AJv3QKOBDXuPsAkQhDUfCmgCWUUIUSBWiSbDQs1g1auicmTT7y1sb74JKilq6ig5nUR1LwmgprXxKVYEzN3R1y13R1wRUIkqEVy5QU1bzhoQhlFCFE8tUg2G9ZTA2Z4Ygy+7fbpsM3623Ke3FCDiwS1SHc9Qc1bkjw1r0kkmw0LNWQzb8weCvBgAMixzlPQsfrTOJeg5g2VFEHN6yKoeU0ENa9JNgUvDbjRx8ZrUSzpRxvLQ7MTR4JaJFdeUDML2VqiiZqfW3rwK5LNhvbU2rJNuxYJapHueoKatzt5al6TSDYrqC3KJwLU8EopkGPHjlUHDhyof2MsJYOg5tUX1LwmgprXpHhKaajRpLbZfekzbMZz584V00dQ89ILal4TQc1rUjylJNRszF0TZN3fuXnlphZOUPMKo4n61Nq6qE+trUeItVJQs9fBuhBLrZdoigpq3jzlqXlN5Kl5TYqnlIIaxpACWCqNp8BzB0HNKy6oeU0ENa/JLCk///nPq1w8ceJEDZfDhw/XQ0bo40pFDHrMyJeyUgBLpfHwYMxz9zmWph7y5a2ph7wmmnpoFoT5k7z++utVLj7yyCM1XI4cOVJdvXo1G7kjjRntHdcUxLppR48eHfXcfa5DUw/58kYTbgh99Jt6H56WT32OPsdHj7mnhqIfL5U3DelYsE/NT38TIAVj7b6mlt5z2lTyQF4iBANahLxQgSME4BKlfAS1hUWUghqntynLu55Zc5155UrARVDzyEATPf1s66Knn209QqyVhBrvsDYBlvpN/16JIKh51QU1r4mg5jUpnlISalw8YEt5bHhoY341a6jQgppXDE1obkUIan76UlDzc6FJaaiRDcasUVl4eMBTUWA29ov73gSWpwhqXh9BzWuiPjWvSfGUCFAzESK58oKalcrWEk3Up7alB78i2eyO8dTwWgAPc6pZ1HxqbcOaYk1Q86rKU/OayFPzmmRTaH4BMTrPmRjy7Nmz9fxqLAW1rGyjbRDUvJSCmtdEUPOaZFOs83zqp39qfqaLQFDzuqCJmp9tXdT8bOuRXePzeHhoUwONDESCWqS7nqDmzVOemtckks2G7lOjuUmcIwhqaZUFNa+LoOY1EdS8Ji6F0fN4aQxvmCMIammVBTWvi6DmNRHUvCYuxSZOpOnJAwGgY089+T3mQwJOHglqkfonBDVnmvU7jupTa+sSyWbDNj/t83i2bD71ZJQ9XtzQkfavvPJKlYunTp2qj3n//fdX3/ve97KROxIFaHHIet99AYnNeGDnYdn8P7+767l9l/131XFslg47Rvec3fW+ebDjNfdv/m4el/SNjY1aE9unu727bvt1l+y33ahZOryGTZvdrr7b/X94qAEwLrIZaJrS18ac/kNG3P/617+ucvH06dObUPv+979f5eJ2Be/z/0gGYlDrk+8p9zGoTXmOvscW1GJAjRtWqszCQy032yvNUrw1LmqMEKn5yTUBtgiBfJSYHaR77eQhkiZj2V33OoeuU4EjhEg2Gx5qOeMhHajloDe0oCNBjTtQpAosqLWtibKhjCKEKFCLZLNhoWbQYqxaKtj2WxFqXJug1i51eWptPWwtCtQi2WxYqFFo9KfxxDMV+GScmp8pZcZNA67y1NqaogmVOEIQ1HwphIaaPfnsemsM5+AhwZgDc9X89MZBiqDmdUETNT/buqj52dYju8aTTXv385577qn4Urm93I4XN+ZYtUhQi+TKC2rePOWpeU0i2WxoT82k40nngw8+WDdHgRxvGYzdJBLUTO32UlBr68GaoOY1EdS8JsVTIkEtkisvqHnTRBM1P9u6RLLZHeGpteWbZk1Qa+tqTxuZVpxmf+lKbPlp57LMmqDmdRfUvCbFUyJBrbQrbw9oeLrcjPRnjt3s71vw0aBGGUUIevrpS0Ge2kITQe2mEKu+GD/01TRvcuulCGpp3QQ1r4ugttAkEtRKufI2M0rTO0v9pkk6d4gGtdLNcdM/CtRK2azp0FwKags1IkGtVPOTmVBSEEulDZlIoGlw6/6OBjU1P9slWcpm27m4ubaroPbaa69VuXjmzJm6Qh85cqS6cuVKNlJ43JUsDlnvuy8d0cwEsWx/tjW3N3+Tt2Xrzf82f+/du7c31Cx/zfM0f6/KQ2q7aZraZrN02D6rzmX7dZd2vdtZapaOGLN05MpwV0Htl7/8ZZWLJ0+erCv04cOHa6BguKkIcKaOnPfChQuTn6d7HXfeeWdvqJ0/f37W/F2+fLmIJl2NWKdsDGyp7XOmUYHnPF/uXKVsNpWfXQW1lKtqaWp+VvUA51RTM5VGc3DOoOZnWm0qcISA1wRgIgRBbVEKglpV2de7UhBrpvF2x9xBUEsrLqh5XQS1hSaRoEY/UKm73qqHBbxzO7eXRhFFgxplFCFEgVpJm+2Wg6C2UERQuykETzVzYGNWFJoZJYKgllZdUPO6CGoLTSJBLUL/BHngzYIDBw5Un/3sZ+sPSs89jKNprtGgVgruTU34HQVqEWzWtBHUFkoIamYS7SXN4BLNzXYu4jU/BbV2CQlqbT0GrVHBIHF34shBB0nsHAlqkfonBDVvLGiiPrW2LpFsdsd5ajx540nc2E/gIkEt0l1PUGtXXtbQRJ5aW5dINrujoEYfD0/fmChSUGsb1VRrgppXVlDzmghqXpOVKUzdjYcG2ADarQy1SK68oOZNE03U/GzrEslmd4SnxlM3vlGAh0a41aEW6a4nqLUrL2vy1LwmkWx2R0CNz+E1P7QiqHmjmipFUPPKCmpeE0HNa5JNQSyanXx8xcKtDrVIrrygZla3tUQTNT+39OBXJJsN7anR7GSm1W7/2bpQ++Mf/1jlIhMfAs+jR49WP/7xj7MRyFKAFoes992XSsOsB8v2Z1tze/M3eVu23vxv83fqf+SDaX9sW/O4q/7b3Nf+z9Jid7ulp/bV1EN+uh/0owJbOZRcNm22ZD5Mk6FjK/e0GT3dGq/r0OzsjmRfF2ovv/xylYsf/OAHa6gdOnSoev7557ORwps6RprGhWl2mPZn6mtedXxNPZS2O6C2Srs5tkey2bCems0YwRTT3bAu1LrHaa5HGqeGp4IhRgjkY+hdb4p8k4dImlBGEQIVOEKIZLMhoYYB0+zkiSdidSPpzW1jFKqgllZRUPO6oImg1tZFUGvr4dZoF9O/1Te6A6yREAlqXH8kr0SeWtugKBvKKEKI4qlFstmQnhp9aIiUi4xXI9r2MYxLUEurKE/N6yKoeU0ENa/JoBT1qQ2Sa1s7C2pePjRR87Oti5qfbT0GrwlqgyVb+w+CmpdOUPOaCGpek0EptzrUIrnygpo3TTShjCIE9an5UgjZp+azOX1KpD61SHc9Qc3bnjw1r0kkmxXUFuUjqHlDJSUC1Hj6+o1vfKP6+Mc/HqIvS1DztiKoeU2Kp0SCmpqfN82Bp+Dnzp1zQ3sYw5galD2XEQE1NT/bakeyWXlqi7KJBLVId71SnhpAY4D1srGKzK1XIshT86pHsllBTVDzFtpIKQU1pptaBjTbxuShcwdBzSsuqHlNiqdE8tQiufKloGbQWrV86qmnZrcdNFHzsy17JJvdVZ7a3/72tyoXP/rRj9aewcMPP1y9+uqr2Uin9dSR/iJmpZj6PH2OTz5u3Lgxa16uXLnSy0sDeHffffeseUMzNKGM+ug39T5Wgac+z6rjR7JZ06SN3eVrs009tDwbw7deu3at+tGPfpSMx48frysS/TgXL15MxkuXLtVPA7lTTxkjTeNSYuqh8+fP94babbfdNmlZpMoZTSij1La506jAc58zdb5INruroLYMg5Gan5H6JzBg7tJzBs63qtlp2xmIPXdAE8ooQqACRwiRbFZQW1hEJKhF6p8oATWKZN++fb3A1pzmfa7KjSbqU2urHclmBbWAUIt01ysFNSqJeWO5pX1drF29pl+Tp+Y1jmSzgpqg5i20kVIKamSB2Y+Zzj0FNYBWYjgH+RLUGgay+CmoeU2Kp6j5mS6CklAjR/SvMWbtvvvuq+68886K71aUaHI21UETNT+bilS1HugSIchTW5RCJKhFuuuVhppVEuAWpdKQD8ooQqACRwiRbHZHQI1mBqLZp9qmKMRIUIvU6SqoeWtDE3lqbV0i2WxoqDGgb//+/a5PhbSx+1MEtbaR2pqgZkpsLQW1LS3sl6BmSixZIhIdxDzap8MYiBHpT6HzmJkaxhw/JailC0NQ87oIal4TQc1rkkwBZqlg3wQdc5YGQS2ldIz51MhZtD41KnGEEKVPTVDbpjUwLQ1e3JijyQW1dKHIU/O6yFPzmghqXpNBKdy1gdqYMzQIaukiENS8LoKa10RQ85oMSrHmZ655Ouhgi50FtbRqgprXRVDzmghqXpPeKTQ9efrJw4Kh4R//+EeVi0888UTt/Z06dar63e9+l414iVPHSNO4lJh6KKUv0x9Fmo5JUw+160Ekmw09pCMFLZqcND0RcWhg6qHvfve7yXjs2LH6uO9973srRFGUBrKBnWsD3BiHhGLzqRnQpnhNRs3PtAmo+el1UfPTa6Lmp9dkZYoBbcyHA82TCmpNNbZ+C2pbWtgvQc2U2FoKalta9Po1NdDIhKCWLgpBzesiqHlNBDWvSTZlDqBxckEtXQSCmtdFUPOaCGpek2TKXEDj5IJasgjqmTGGdrqmj7S9VPIATCIEQc2XgqDmNXEp9t1HPoSy7CkUYo4RBLW0ivLUvC6CmtdEUPOauBRegWLoxqo41vufgporgjpBUPO6CGpeE0HNa+JSmJEDoVbFsZpGgporgjpBUPO6CGpeE0HNa1I8RVBLF4Gg5nXhu6QvvfSS31Agha6ZCEFQi1AKnTwIah1BFquC2k0haBHYB6+bXSLnzp2reHWvVBDUvPJoMrQFV+yNAp/98VIEtbSWglpVT07KpKRNmDV/8y5yKbAJat5uBbWFJoKaNw5SdjvUbAKFJsRSvx999NG0gBOnCmpeYEFtoYmg5o2DlN0ONd4zTkEslTb2dzPSJdJOFdTaerC2q6D2n//8p8rFT3ziE7Xxnj59uvrTn/6UjbTVp46RpnHZ7VMPPfbYY72hdunSpclto2t7VoG76XOvR7JZ08TjLp+yY/vUmHroa1/7WjLef//9tfFq6qGdO90Mxjx2TH3NLOWlkcaDhLHPr+OtV6ZAfUjYsVBbdpFqfqbV2e3NT3uzJQeyZvqYMzGnS8OnAr0IQUM6IpRCJw+CWkeQxepuh5pNHd+EV+63+tRivJsL6OWp6YX2NNH0oKDWZdkre295y1vqbouxXtfLFkRmgzw1L4ygttBEnpo3DlJ2u6eGBtz1Dx48mH1gcPbs2bR4M6QKal7kHQE1jIo2ezPg6lPhiGO4/YJaU92t34LalhZ4Y0244cFNMbX81hlX/xLUvEahocbAR2CD8diIbfo4Uk+kePJk+/jLXJ0iqKU1EtS8LmjSvcn6veZJEdS8zmGhhvcFvHj6RABYjNrG1Wcb64yNafZ3ALZ1QySo/fCHPyzuAZiOFy9erF577TVbLbYkD+QlQsA7o4xKh//973/1EJLS+eD8V65cCWOzQG1o623yIR14Y/v27Wt9Bg+3P9d3Qbo9kVrn03kUiqCWrhrPPvtsGKhduHAhncmZUwU1L7ig5jXZTIGwAKo55odpvfl4ca55SZ+bQY191wmCWlo1Qc3rIqh5TbYLNZwR6u7GxoY/+MCUUJ4acGI2hCaYuNgu5FLXaM1QlusEQS2tmqDmdRHUvCbbhRpHtDGBMID6uC7gQkENIHU9MpqhxFWBJ1PAT1BbpdSw7YKa10tQ85qMATWOamCzltc6gAsDNfPI7MEAF8gTJnsw4GVspwhqbT3GWhPUvJKCmtdkLKhx5C7YhgIuDNSs+Tj0qYXJa1DLPUyw/XJLNT/TyghqXhdBzWsyJtQ4eg5sXcClhtaEgJp19PdpZno5b6bYi8fAbZ1gUCMPTz75ZNF49OjR6vDhw0XzYBrw1PnkyZPF80IeyIvlq+SSsqGMSuaBcz/xxBMVs8qUzgfnP3LkSHXo0KFR83LfffdtPgA0mKWWDP1iWnVziEJAjTsfmV23PwyI2Uhvu7ChYDOopURT2upPFUojaRTBBmBIE3B9OTD6ODVrOjafevbNDPsx1ANBt+PpGdTuuuuu+ukreSkVH3jggep973tfsfM3r/vee++tzpw5UzwvH/7wh2vvtZm3Ur8pG8qo1PntvJ/+9KcrPvZt6yWXU9gs3nAfUFLvaamZQxPCU7PBs82HBEOgZu3vdZuenMughitdOkR6o0B9at4a1KfmNZm7T60LsmaOQkDNHhKs2/zkAml+bicIamn1BDWvi6DmNRkTauakdL20ZSBr5igE1HCbuQDGpAwN1h+Xegoy5FiCWlotQc3rIqh5TcaCWhdojFuFD0PqdwioGZgA25B3N2lDA0KE2G4Q1NIKCmpeF0HNazIG1AxoBrIhLGjmKATUbEgHUOPxbJ8wJtA4n6CWVl1Q87oIal6T7UINgOGRrQuyZo5CQI0M2TgzwAZgci+vsy8XTvt6DAFMDEHNlGgvBbW2HqwJal6T7ULNH3H9lDBQA2I21sw8thdffLG6fv16PZ0ySybns0fYeHdjBkEtreZzzz0XZuoh8hIhCGq+FAQ1r0mdAtiaHhtws2jt7CEdhpnTJJMjQY1rBOARgma+9aWgmW+9JlPbLMO1mATWxqLRSmOdPnUcHbwza93xe6jTM/rg265EZA6R6DhkSZw6CGpphQU1r0tpqFGxmQWaCs1NnyXrVuF9jqdPmRpq1orjSmy0BNdON5Q5PjbONSTUpi8CfwZBzWtCiqDmdSkJNXtCaBW5uRxrJIC/4tUpU0PNrpN6Squt2Z/Ob9tOTgW1RXkJamnDFdS8LqWghidmlXfZsoTHNiXUOLZdL0BLNS1tO9sENUHN19pGiqDWEGPxsxTU7HVCq8C55brTb/kr7Z8yJdTs3XCul/N0A91VpgXbBLWFQvLUuqZyc11Q87qUgppV3D5Ln+tpU6aEmsE89xqleXL0rxF2FdSuXbtWfeUrX0lGm7uJ+akQRVEaRLKBp59+etMb6QO18+fP3zI2bA9EmD8uVSYf+tCHam0OHDiwuT3VRF2G9cmffi47+Xa2/fe//61y8ZOf/GQtDFPcvPHGG9mIWFNHOj4vX748+Xn6XAf5uHHjRvG8kIdImlBGffQbc58+MLN9xjxvn2NNZbOvv/76Jsz5ncrLiRMn6n14+sl2wMdySNixUFt2kWp+ptVR89PrUqr5acMaDFy5Za6Z5q9kvJSpmp/2ZHPZLDw2rMP62wS1RbkKam0Dp/OVtzhoxly9erW9scAad15gEiEY1BhesU4FWvcarO8oBzNLt8q97nnW+R/n/OIXv1jbDHZDHCPYQwIbg9Y9ZvchAdvXKRN5al1lR17HQEpVYOBhgLdKwpJ+DV5bKxWiQY1XpUyfOSFildzO3V2yfe7AOd/+9rdv6mF5GiMfNtciN5BUSHlygtpCKavIEWa+LQU17nq48owF4s5IPvDUvv71r2+O3MaISoRIUPvqV79a7d27d/Nd5TmhhvaUgTW5DCCsz50P8mKj+2kefu5zn6v7srCjsfKCLXKNubF3BnnyYUFQWyghqN0UggoDQCzgMbJOxLhK9NeQl0hQ42tSb3vb22q4oMlYFdg077sEHtgtyxLBgMISDcZuXdhgY8CWCylPLjTUKCyaPLywanckXmIl02MHQS2tqEGNrdZRnd5z2tQoULPmzpe+9KW6IpeEGopPURf6liSwsQ78KaBmr4Qtu5GmPLmwUIPSTBiJ0SAcdwOiVSzgNmYQ1NJqdqG27K6ZPsI4qRGgRh7oW8RToxITdyvUDDjW1zUF1NCb47LMBSuH5vawUMNLg9BkuhusHU9n7VhBUEsraVDDsKjAzb6L9D+mSeX8YzdvhuYUe6Tvij41q0y7FWrW9LS+rpdeeqnufx3rqefQsmnuHxZqzUx2f1tbe8wKJqh1Vb65blCzG0nqJpP+57ippaFmTzu5fjTZ7VCzvizqYrN7CMiXflK+I6FGdUG8MV/cFdTSEKICX7p0qdY7N1Yo/c9xU0tCzW6idv2CWlW3ogxgeG3MfGu6GPBKPSnfkVCzzlrEHCsIamkleUyP8VqHcHqv6VNLQo1rb16/VV68NbQp5b2iOhW4RDBwWReQebDkha4j+l77fkRp7PzvSKiZoBj6WEFQ80riodx2223Ve97znmLDBixXpaCGdwa47HsZ9pYF68TmtjHt0a571bI01Cx/TaiRZnXUts+53HFQs6cu1hQYSyxBra0kQKNv5F3velfFi8SlQymoWeUEXqvimC2HvnpHhZrdDEqBfuh5i70mZX0bzaZA38JnP6Ye+ta3vpWMR48erY1WUw89UzHNzVvf+tZ61PytNIUNABgamfuf4UOpaB3kLNnOjXHo8Xfq/jbdD7aSugYbjpXaNkfa6FDDFV0n48syYp4DQGdtCHoAAAZBSURBVFt3BPU///nPKhd5PYo78alTp6rf//732Ugep470GZaaZufll1+u3vnOd9ZNTjw0TT3kyxtNKCM6x7EZllPbRO741LPctinTX3nllfra3//+99fnb9qsbWOOwinzkDu2aTLE4VnpqXEywDY05mA1BtBWXaCan1X9fh1NTirquXPn6hsTnor9thuVDbhcpemY27EpOugjBD0ouFkKNlYNG2GcGuP3NjY2NgfNU/9LhEmgNuaFzAE08iuoVfUbG6v6jdhOP9PcQVBLK04FLhkMbE274clniRuf6RAaanMBDTEEtZsvjXe9a/rUaF410ymXuUNEqM2tQep8paFGnigb3oXFY8NOci2uVP6nSAsLtTmBhrCCWtq8aGphtKWDoJYugQhQI2fALEr3QFio9X2UPtZjdEEtXWkENa+L9an5LfOnCGpe87BQo00OsFZF7hBjBEEtraKg5nUR1Lwm8tS8JsVTBLV0EQhqXhdBzWsiqHlNiqcIaukiENS8LoKa10RQ85oUTxHU0kUgqHldBDWviaDmNSmeIqili0BQ87oIal4TQc1rUjxFUEsXgaDmdRHUvCaCmtekeIqgli4CQc3rIqh5TQQ1r0nxFEEtXQSCmtdFUPOaCGpek1lSmHro6tWryWiDfZlG5uLFi8nItNYY9NSRyQcvXLgw+Xn6XAf5YFaKPvtOuQ95iKQJZTTl9fY9NgNN++475X6RbDbs4NspKPfmm29Wufj444/Xs1OcOHGievXVV7OR13Wmjs1pXKY+16rja+ohX9429dAq7ebYbhV4jnMtO0ckmzVNhjBk5dRDQw4WZV81P9Mlwd0dYy4dyAN5iRDIB82tCIEKHCGo+RmhFDp5ENQ6gixWBTWvi6DmNRHUvCbFUwS1dBEIal4XQc1rIqh5TYqnCGrpIhDUvC6CmtdEUPOaFE8R1NJFIKh5XQQ1r4mg5jXpnYJ4fLlHn8jrLdm2dhTUvHyCmtdEUPOa9EphmmD79NbY8+TLU0sXgaDmdRHUvCaCmtekV8rZs2erffv21R/+ENR6SbbtnQQ1L6Gg5jUR1LwmK1MY3McXa1gCNEFtpWSj7CCoeRkFNa+JoOY1WZrCwEu+R4mnRhDUlso16kZBzcspqHlNBDWvydIUIEaz0z69JagtlWvUjYKal1NQ85oIal6TbMoLL7xQNzsRzYKgZkpMvxTUvMaCmtdEUPOaJFP49if9aN3hG4JaUq5JEgU1L6ug5jUR1LwmyZSDBw9WxG5YF2pMPZSLDz30UA3QQ4cOVc8//3w2YtBTx0jTuGjqIV/eaKKph9q6RLLZSWbpgNoceGhszgaBd4aXhrfWDetC7c9//nOVix/5yEfq8x07dqz6yU9+ko1c29QRaGIkU5+nz/HJx8bGRvG8kIdImpi31kfDKfehjk15/L7HLmGz169fT177JFADTvSFrfoQcXM7Hy+2BwHW7GTCxhQYGYBLtG1d6K2zrsG3adUw1ubNJr3X9KnkgbxECAa0CHmhDkQIwC9K+UwCte2KjEB4aX3jds/H/wW1tIqCmtdFUPOaCGpek0Ep6zY/l51EUEurI6h5XQQ1r4mg5jUZlCKoDZJrWzsLal4+Qc1rIqh5TQalCGqD5NrWzoKal09Q85oIal6TQSk8VCCOGdT8TKspqHldBDWviaDmNSmeIqili0BQ87oIal4TQc1rUjxFUEsXgaDmdRHUvCaCmtekeIqgli4CQc3rIqh5TQQ1r0nxFEEtXQSCmtdFUPOaCGpek+Ipglq6CAQ1r4ug5jUR1LwmxVMEtXQRCGpeF0HNayKoeU2Kpwhq6SIQ1LwugprXRFDzmsyS8otf/KLKxZMnT1bveMc7KqYe4mX8XMSgp46RpnHR1EO+vDX1kNckks2GfKF9KsIx+8eyeOXKlWpV5I6kKA1kA+VtIDf1EOlDw56hf9D+UkAKSIHICghqkUtHeZMCUmCwAoLaYMn0BykgBSIrIKhFLh3lTQpIgcEKCGqDJdMfpIAUiKyAoBa5dJQ3KSAFBisgqA2WTH+QAlIgsgKCWuTSUd6kgBQYrICgNlgy/UEKSIHICghqkUtHeZMCUmCwAoLaYMn0BykgBSIrIKhFLh3lTQpIgcEKCGqDJdMfpIAUiKzA/wHz2cVy1LaLJwAAAABJRU5ErkJggg==[/img][br][br]Define [math]M[/math] recursively using function notation.
Write the first five terms of each sequence. Determine whether each sequence is arithmetic, geometric, or neither.
[math]a\left(1\right)=5[/math], [math]a\left(n\right)=a\left(n-1\right)+3[/math] for [math]n\ge2[/math].
[math]b\left(1\right)=1[/math], [math]b\left(n\right)=3\cdot b\left(n-1\right)[/math] for [math]n\ge2[/math].
[math]c\left(1\right)=3[/math], [math]c\left(n\right)=-c\left(n-1\right)+1[/math] for [math]n\ge2[/math].[br]
[math]d\left(1\right)=5[/math], [math]d\left(n\right)=d\left(n-1\right)+n[/math] for [math]n\ge2[/math].
Here is the graph of a sequence:
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATAAAAFuCAYAAAAGf0R0AAAgAElEQVR4Ae2dW4wfVeHHQUSCiG30QQ2J2yfRxGT7ZNSX7ZtX3D5qIu764us2MSYq0V2DJoYHFhGkQNutvdDai/ZeCm23N9ouhd5rtVzachUsVIIIKvX88x3+Zzg7OzO/mfme+c2Z3e9JTmfm3ObMZ2a+/Z7z+/3OXmUUREAERKClBK5qab/VbREQAREwEjA9BCIgAq0lIAFr7a1Tx0VABCRgegZEQARaS6CrAnbVVVeZZOzr64vg/elPfzJz5841OO7p6TFjY2OthaqOi4AIdIdAVwUseUkDAwOxUEGwLl++HBXBdtasWfFxsp6ORUAERAAEGhMwiBSclhWt5O2AExsfH5+U/N///te8/fbbk+Jrr71m0uJbb71lFMVAz0C7noFJL3yBg8YEbHh42CCmhfPnz0cOLJkHATt48OCk+OCDD5olS5ZMips2bTLbt28PIq5atcqsWLEiiL5kMVm2bJnZtm1bsH0Ew5UrVwbbP3ANneFDDz1kELOegRDSt27dmnzlOx43ImBwXbNnzzYQqrTQ29trMCdWJNg5tCJlmyjz17/+1Zw6daqJUxc+J1hfuXKlcPluF/zLX/5iTp8+3e3TljrfH//4R/O///2vVJ1uFv7zn/9szp49281TljoX2BV9592GGxEwzHdh/istuPNiafluGgQQHwpUuXC3nTr3JWA8XQkYz1ACxjOMW8DcV5r7KiNeaGx0dDQSsCwxjE/Y4I4EjIcvAeMZSsB4hlELcF9pwz6I0ODgoNmzZ08c00TO7cbnPve5SMBuvPFGNzmofQkYfzskYDxDCRjPMGphaGhoyqeLyICoJWPed8Hs8NF+ryzUYaQEjH9wJGA8QwkYz9BrCxDCa665JnJgV199deacmteTVmhMAlYBWqKKBCwBpMKhBKwCtDqr3HTTTZF4WRG74YYb6jxd5bYlYJXRxRUlYDGKyjsSsMro/Fc8duxYJF6f/exno+1Xv/rVaBviMFICxt9/CRjPUALGM/TWAoaP+K4YxAFzYEePHo2GkCF+GikB42+7BIxnKAHjGXprob+/P/oJ0t/+9rdYwNA4hC20IAHj74gEjGcoAeMZemkB3+K3v59MChhOYPO8nMxDIxIwHqIEjGcoAeMZem8hTcC8n4RsUAJGAjTGSMB4hhIwnqH3FiRgfpDiww/9FpJjqd9Ccvxa9VtI7lLfry0Be58FsycBY+i9V1cCxjGUgHH8aqutISSPVkNInqGGkDxD7y3IgflBKgfGc5QD4xjOCAeGBQ3xJVYbd+3aFX2N4o477jBr1qyJI9L3798fRIQ4rFu3Loi+ZDG5//77zb59+4LtIxiuX78+2P6Ba+gMIbCIWc9ACOm///3vS6tgI+uBle7l/1eAgLnLR2OBNnyRdcOGDebcuXNxvHDhgnnllVeCiBMTE+bAgQNB9CWLCVY8hZvNym86HQyxEm/T/cg7P1Y7zctvOu/w4cMGsel+5J0fz2HZ0CoBS16chpBJItWONYSsxs2tpSGkS6P8/owYQiaxSMCSRKodS8CqcXNrScBcGuX3JWDlmXWlhj6F5DHrU0ieoT6F5Bl6b0EOzA9SOTCeoxwYx1AOjONXW205MB6tHBjPUA6MZ+i9BTkwP0jlwHiOcmAcQzkwjl9tteXAeLRyYDxDOTCeofcW5MD8IJUD4znKgXEM5cA4frXVlgPj0cqB8QzlwHiG3luQA/ODVA6M5ygHxjGUA+P41VZbDoxHKwfGM5QD4xl6b0EOzA9SOTCeoxwYx7BVDgx/VXvPnj1RTLts5GPFiU5BAtaJULF8CVgxTnmlJGB5dDrntUbA8JeDenp6zPDwcBTTLg1/Mq2vry8ta1JayAKGPy6yYMGCaLUMrJhx6623BvcHRyxMCZglUX0rAavODjVbIWDj4+ORMOX95SAIHP6+Y9sF7JZbbjHXX399LGDXXXed+fKXv8zd5ZpqS8B4sBIwjmErBAx/zxEvS1aAwKGMFbpkOawHBtdl46lTpyKBWL16tTl+/HgcMXH+3HPPNRrhutLiY4891mi/0risXLnSYA21tLwQ0rCe2t69e4PtHxgtX7486P5hwUpwDOF+pvXh4sWLBs9h2dDV9cAwNBwdHY1ECvuDg4PxsAquDGnY5gnYmTNnjI24KRAJtLlx48Y44kY9/vjjjcXdu3enihf6unDhwsb6lcXkwQcfNFg0MCu/6fQtW7ZE97bpfuSdP3SGmzZtMoh519B0XvArsuIFxtyXDRgqQnwQXHeWJWC2nt2GPAd28803TxGxG264wXY9qK2GkPzt0BCSY9iKISTmtfAJow1WqPACzZkzx4yMjEQRzswe27Jp25AFDJ+ifuITn5gkYmNjY2mX0XiaBIy/BRIwjmErBAyOy50DwwuNSXsImf1UEluUs59U5mEJWcDQbwyHly1bZpYsWTJJuPOuqYk8CRhPXQLGMWyFgMF9QZiWLl0aReynfd/LOrNOSEIXMPRf38TvdBc75+ub+J0ZdSqhb+J3IlQwHyKGeS84LXc46VZHepHhlgTMpVZ9Xw6sOjtbUw7Mkqi2bYUDq3Zp2bUkYNlsyuRIwMrQSi8rAUvnUjRVAlaUVJfLaQjJA9cQkmeoISTP0HsLcmB+kMqB8RzlwDiGcmAcv9pqy4HxaOXAeIZyYDxD7y3IgflBKgfGc5QD4xjKgXH8aqstB8ajlQPjGcqB8Qy9tyAH5gepHBjPUQ6MYygHxvGrrbYcGI9WDoxnKAfGM/TeghyYH6RyYDxHOTCOoRwYx6+22nJgPFo5MJ6hHBjP0HsLcmB+kMqB8RzlwDiGM8KBYUVW+8dAsMWLhzXGbrvttmihQCwWiLh27VqzYcOGICIWacPvOkPpT1o/7r777ohlWl4IaWCIBQBC6EtWH8AwKy+EdDBEDKEvaX3Au4z+lQ1dXZG1bOeS5a9cuWLc+NJLL0UCduTIEQNxc6Nbrsn9s2fPmpMnT07qd5P9STs33APYpeWFkIbhD5YPD6EvWX1Yv369effdd4PtI1YxBses/jedDnZ4DsuGVglY8uI0hEwSqXasIWQ1bm4tDSFdGuX3Z8QQMolFApYkUu1YAlaNm1tLAubSKL8vASvPrCs19Ckkj1mfQvIM9Skkz9B7C3JgfpDKgfEc5cA4hnJgHL/aasuB8WjlwHiGcmA8Q+8tyIH5QSoHxnOUA+MYyoFx/GqrLQfGo5UD4xnKgfEMvbcgB+YHqRwYz1EOjGMoB8bxq622HBiPVg6MZygHxjP03oIcmB+kcmA8RzkwjqEcGMevttpyYDxaOTCeoRwYz9B7C3JgfpDKgfEc5cA4hq1wYPiL2yMjI5Ni8rKxcoMtk8xLHkvAkkSqHUvAqnFza0nAXBrl91shYBCnvr4+Mzw8HEf3Unt7e01/f78ZHx+PopuXti8BS6NSPk0CVp5ZsoYELEmk3HErBMwKV9qljY6OmoGBgbSszDQJWCaaUhkSsFK4UgtLwFKxFE5sjYDBhaUFODM4r8uXLxsMNdMC1qzCpLiNBw8ejNYDu/fee83DDz8cx4mJCXP8+PEgIvq1efPmIPqSxWTx4sXm6NGjwfZx+/btZsuWLcH2D1zB8NixY8H2cdu2bQYcs56BptPBLvgFDeGyMEyEWPX09JgFCxbEOoWVVefPnx+5MAwjUQ5i5gYI2PPPPx9HXDTqLVu2zBw+fDiOWPzu6aefDiLu3bvX7Nq1K4i+ZDEBv6y8ENLbwBAvXwissvpgp2Wy8kNIX758ufu6F9pvdEFDCBlEDQFCBMg2DA0NxXk2LbnVEDJJpNqxhpDVuLm1NIR0aZTfb8UQMnlZ7pwYHJcbIGad5sQkYC6x6vsSsOrsbE0JmCVRbdtKAcNQ0TowiJU7PyYHVu1BqFJLAlaF2uQ6ErDJPMoetULAIFKDg4PR97zmzZsXzYXZC8V8F1wY5sVQJm0OzJa1WzkwS4LbSsA4fqgtAeMYtkLAcIl2MhET8GnB5qflJdMkYEki1Y4lYNW4ubUkYC6N8vutEbDyl5ZdQwKWzaZMjgSsDK30shKwdC5FUyVgRUl1uZx+zM0D14+5eYb6MTfP0HsLcmB+kMqB8RzlwDiGcmAcv9pqy4HxaOXAeIZyYDxD7y3IgflBKgfGc5QD4xjKgXH8aqstB8ajlQPjGcqB8Qy9tyAH5gepHBjPUQ6MYygHxvGrrbYcGI9WDoxnKAfGM/TeghyYH6RyYDxHOTCOoRwYx6+22nJgPFo5MJ6hHBjPkG4B64G98cYbccQaRliGB4sGvvDCC3F88cUXo7XE8PvKpiMWCsRaZU33I+/8f/jDH8ylS5eC7eMTTzxhsEhl3jU0nbd69Wrz+uuvB9vHI0eOGMSmOWWd/7XXXjN4DsuGRtcDK9tZCJi9EdhCuCBgv/rVr8yKFSviuGPHDrN79+4g4tq1aw0e7lD6k9aP++67L1p0MS0vhDQwxMMdQl+y+gCGWXkhpK9Zs8aAYwh9yepD8CuylhWsTuU1B9aJULF8zYEV45RXSnNgeXQ652kOrDOjRkpoDozHrjkwnqHmwHiG3luQA/ODVA6M5ygHxjGUA+P41VZbDoxHKwfGM5QD4xl6b0EOzA9SOTCeoxwYx1AOjONXW205MB6tHBjPUA6MZ+i9BTkwP0jlwHiOcmAcQzkwjl9tteXAeLRyYDxDOTCeofcW5MD8IJUD4znKgXEM5cA4frXVlgPj0cqB8QzlwHiG3luQA/ODVA6M5ygHxjGUA+P41VZbDoxHKwfGM5QD4xl6b0EOzA9SOTCeoxwYx7B1DmxsbMwMDQ3FV41lNkZGRsy8efOiiJeqU5CAdSJULF8CVoxTXikJWB6dznmtErBjx46Z/v5+09fXF1/ZwMBALGjnz583PT09BuXyggQsj07xPAlYcVZZJSVgWWSKpbdKwHp7e83o6OgkAYOYjY+Px1ebPI4znB0JmAOD2JWAEfD+v6oEjGPYGgEbHh6OxAti5TowvEQQNrgviBv2kwELGj7++ONxtAsa3n777WbZsmVx3LZtm9m5c2cQEQvJrVq1Koi+ZDH53e9+Zx599NFg+4jFDENneO+99wbLD/cdi2qCY9Yz0HQ6nr/gFzR0Rcvdt0KFYeSsWbPM7NmzIyGz6XYLAXvzzTfj+Mwzz0Qrsj7yyCPmpZdeiuPLL78cLzvtLkHdxD6WlIboNnHuoueEyGIOsmj5bpdrA0MIxD/+8Y9gGWJZ7ieffDLY/oFd0EtK4wWBq8IWISlgmNCHgNk8zYFFKLryj4aQPGYNITmGwQ8hIVhYvz4t4tKR7gZ8SonhZl7QHFgeneJ5ErDirLJKSsCyyBRLD17AkpeRdGAYOrqfOsKNYS4sL0jA8ugUz5OAFWeVVVIClkWmWHrrBQyChmEjvgc2d+7ceDiZd/kSsDw6xfMkYMVZZZWUgGWRKZbeOgErdln5pSRg+XyK5krAipLKLicBy2ZTJEcCVoRSA2X0W0geun4LyTPUbyF5ht5bkAPzg1QOjOcoB8YxlAPj+NVWWw6MRysHxjOUA+MZem9BDswPUjkwnqMcGMdQDozjV1ttOTAerRwYz1AOjGfovQU5MD9I5cB4jnJgHEM5MI5fbbXlwHi0cmA8QzkwnqH3FuTA/CCVA+M5yoFxDOXAOH611ZYD49HKgfEM5cB4ht5bkAPzg1QOjOcoB8YxnBEODOuBPf/883HEOlFYxQILoR06dCiOp06dMk8//XQQcc+ePdFigaH0J60fWAzy3LlzQfBK6x8Y7tq1K9j+oc94Bp966qlg+7h7926DmMY3hDSww3NYNkxew6Zs7S6Xh4DhRbMRogUBw4qiWNTQxomJCXPixIkg4o4dO8zWrVuD6EsWk8WLF5vjx48H20esvCuG3POMVYrBMesZaDodz1/wK7L61jsNIf0Q1RCS56ghJMdwRgwhk4gkYEki1Y4lYNW4ubUkYC6N8vsSsPLMulJDn0LymPUpJM9Qn0LyDL23IAfmB6kcGM9RDoxjKAfG8autthwYj1YOjGcoB8Yz9N6CHJgfpHJgPEc5MI6hHBjHr7bacmA8WjkwnqEcGM/QewtyYH6QyoHxHOXAOIZyYBy/2mrLgfFo5cB4hnJgPEPvLciB+UEqB8ZzlAPjGMqBcfxqqy0HxqOVA+MZyoHxDL23IAfmB6kcGM9RDoxjKAfG8autthwYj1YOjGcoB8YznNTC0NCQ6evri9MuX75s5s+fb3p6eqI4NjYW52XtyIFlkSmXLgdWjldaaTmwNCrF01rlwMbHx01/f/8kAYOgDQ8PR1cMMYOQnT9/PpeABCwXT+FMCVhhVJkFJWCZaApltEbArDjhpXEdWFKwIGijo6OTLh7rgbnxxRdfjNYDw/pf77zzzqTolmtyH9Yday012YdO58bL9+9//zvYPp45cyZ4huvWrTP/+c9/gmWIRT5Pnz4dbP/ADs9h2VBoQUOIztKlS83IyEjsiuCOOjmktM7AecGBIboChoUJ3QA3Zh2ZTceLuHfv3jhCBFHvtttuM/fff38c169fbzZu3BhEXL58ecQulP6k9ePuu+8OglVa35AmhvyzjMUCseJpFuMQ0mtZ0PDYsWNm9uzZpre318yaNSsSHggKxGPu3LlWWwptMa8FZ4XQScDQPsQuL2gImUeneB5YX7lypXiFLpfUJD4PfMZO4kO47IQ6HBOEx4aka7LpaVu4tTlz5pgNGzYYrHF+1113RQKIfYRkW2kOLNmuBCxJpNqxBKwaN7eW5sBcGuX3a5sDc4WFETA4OdS30To6HCPgGGVsGBgYiIXTpiW3ErAkkWrHErBq3NxaEjCXRvn92gTMnVx3BQwPPUSnakgOIeHyBgcHDebbkIfzYj8vSMDy6BTPk4AVZ5VVUgKWRaZYem0CBmGBmGDohzkvDP0woY95MTz4VQPclp0Ps21g2AiRxNyX68ZsfnIrAUsSqXYsAavGza0lAXNplN+vTcDQFStiGE4iQtDsvFj5rvqrIQHzw1ICxnOUgHEMaxUwrmv11ZaA+WErAeM5SsA4hhIwjl9ttfVbSB6tvkbBM5yxX6PAnNS8efMyI4+2egtyYNXZuTXlwFwa1fblwKpxs7Vqc2D4RNCNmPvC5DvmwZI/9bGd6dZWAuaHtASM5ygB4xjWJmBZ3Up+DSKrXJ3pEjA/dCVgPEcJGMew6wKG7rpfcuW6X622BKwat2QtCViSSPljCVh5Zm6NrgsYfhokAXNvQfq+JvHTuZRJ1SR+GVrpZWfsJD6+XIpVKJIRv2vEz32aDHJgfujLgfEc5cA4hrU5MHwKmYwQrqYn8IFLAsY9NLa2BMySqL6VgFVnh5q1CRjXrXprS8D88JWA8RwlYBzDGSFgWNAQK0vaiKV4MA935513Rr/LxIuIuG/fPnP48OEg4ubNm6M+hdKftH48+OCD5tChQ0HwSuvfpk2bot/ipuWFkvbAAw8Eyw+M7IKFofBK64eXBQ3PnTtnbrrppsKR091ytSFgr776ahyx1DAEbO3atbGoQdyeeuop88ILLwQRDx48GK0gG0p/0vqxcuVK89xzzwXBK61/jz32WPSfUlpeKGkrVqwwzz//fLAM9+/fb8AxFF7JfoAdnsOyYfI6zsYYCNi2bdsKx7In9FleQ0g/NDWE5DlqCMkxnBFDyCQiCViSSLVjCVg1bm4tCZhLo/x+rQKGhQUx35QWy3fVXw0JmB+WEjCeowSMY1ibgOG3j5hnSkb8gY9Of3SDu6TOtSVgnRkVKSEBK0Ipv4wELJ9Pp9zaBAw/2sYDjoDvgyHAkRVZsz4qXOM/EjA/cCVgPEcJGMewNgGD87IBAmaXeoaIQdyaDBIwP/QlYDxHCRjHsDYBw1DR/nEN/KzIujF01xU3rvvVakvAqnFL1pKAJYmUP5aAlWfm1qhNwNyhIpbQwV8iwh/4WLBggRyYewcy9vVj7gwwJZL1Y+4SsDKKztgfcyd5YDFDuDIMHyFoTQY5MD/05cB4jnJgHMPaHJid8+K6V09tCZgfrhIwnqMEjGNYm4Bhngt/DxJ/C9LOhXFd9VdbAuaHpQSM5ygB4xjWJmAQLSydg7kviBn+ejbmwEIIEjA/d0ECxnOUgHEMaxMwt1tYhdX+QQ8saIiJ/LIBbeAb/WlDU4hlVl7aeSRgaVTKp0nAyjNL1pCAJYmUO+6KgNkuQXzwp9bKfo0C39yHk8PXMfCdMrRhA9JsHrZwep2CBKwToWL5ErBinPJKScDy6HTOq13A4JzguOC88AkknBjSyoRkeQiV/SQz6chwjmT55LkkYEki1Y4lYNW4ubUkYC6N8vu1CRjmvzCJD7cFB4WH3VeAgCWFy7adlof1wC5duhRHfLcF/cKcHL5vZeOzzz4bLTcNgWs6TkxMmAMHDjTejzwOq1atMi+//HKwfcTid1jLKu8ams7DWlYhM7QLVjbNKev8YIfnsGx4/3dCGTUhJBAxX59A4sfh+AMhEEMMG9OC/cJsMg8Cdvz48Tju3r07ErA77rjDrFmzJo5Ih2iEECGu69evD6IvWTzuv/9+gwXvsvKbTm8Dw4ULFwbLD/cPDhHmo+l7mXd+LyuyJkXD9zEEDMKFb/hDxJLCiOM095XWD6g5HNjRo0fTsoNI0zfx+dugb+LzDPVNfJ7hlBYwj+a6MIiX+4PxKRUSCRKwBJCKh5oDqwjOqaY5MAdGhd3a5sAq9KVwFYiXFbCy4oWTSMAKo84tKAHLxVMoUwJWCFNmoVYIGByXXdUV3+zHJ412Eh/Dxvnz50/6A7r2E8qsq5aAZZEply4BK8crrbQELI1K8bRWCJid/4LrwgcD7tckrBtztxKw4g8AU1ICxtB7r64EjGPYCgHjLnFqbTmwqUyqpEjAqlCbXEcCNplH2SMJWFliXSqvTyF50PoUkmeoTyF5ht5bkAPzg1QOjOcoB8YxlAPj+NVWWw6MRysHxjOUA+MZem9BDswPUjkwnqMcGMdQDozjV1ttOTAerRwYz1AOjGfovQU5MD9I5cB4jnJgHEM5MI5fbbXlwHi0cmA8QzkwnqH3FuTA/CCVA+M5yoFxDOXAOH611ZYD49HKgfEM5cB4ht5bkAPzg1QOjOcoB8YxnBEODAsauguibd68OVoP7Oc//7lZtGhRHLEA3tatW4OIWKlz+fLlQfQli8k999xjtmzZEmwf28Iwi28I6StWrDCIIfQlqw+tWNCQ0WkI2DvvvBPHixcvRgKG1UTfeOONSfHtt982IcTTp09HCy6G0JesPqxbt8689dZbQfBK6+OpU6eCZ7h27Vrzr3/9K1iGWMn4xIkTwfYP7PAclg0dl5Qu22A3y2sI6Ye2hpA8Rw0hOYYzYgiZRCQBSxKpdiwBq8bNrSUBc2mU35eAlWfWlRr6FJLHrE8heYb6FJJn6L0FOTA/SOXAeI5yYBxDOTCOX2215cB4tHJgPEM5MJ6h9xbkwPwglQPjOcqBcQzlwDh+tdWWA+PRyoHxDOXAeIbeW5AD84NUDoznKAfGMZQD4/jVVlsOjEcrB8YzlAPjGXpvQQ7MD1I5MJ6jHBjHUA6M41dbbTkwHq0cGM9QDoxn6L0FOTA/SOXAeI5yYBzD1jiwY8eOmbvuustgxYisgL/YjXKdggSsE6Fi+RKwYpzySknA8uh0zmuFgA0NDZmBgQEzPDwcbXt7e6dc2eXLl01PT4/p6+ubkpdMkIAliVQ7loBV4+bWkoC5NMrvt0LAIE5ugICNj4+7SZGwQegkYJOw1HogAePxSsA4hq0QsOQlQsDcoSJepP7+/kjU0gQM64E988wzcZyYmIjWA3vggQeiOhBDxKNHj5ozZ84EER999FGzffv2IPqSxWRsbMxgza2s/KbTH3nkEfPwww8H2z/wWbJkicHab02zyjo/GCJm5TedDnatWtAQQuMOIeHOcIwt8rIE7MKFC8bGJ554IhIwPDxY1NBGLN6GT65CiLt37zY7duwIoi9ZPPDg4FOqrPym03ft2hW9fE33I+/8S5cuDZYf+r1z584o5l1Dk3lnz55tj4DBdWGey3VfECwIF0KWgCUdnObAkkSqHWsIWY2bW0tDSJdG+f3WDCHTxAtDmDlz5piRkZEoDg4Oxsd5KCRgeXSK50nAirPKKikByyJTLL0VApYmXrg8fG0CrsvG0dHRaDhpHVkWAglYFply6RKwcrzSSkvA0qgUT2uFgM2aNcvMnz8/dlpwXHBfyaAhZJJIvccSMJ6vBIxj2AoBsw7L3brzYBYBJvLT0m2+3cqBWRLcVgLG8UNtCRjHsBUCxl3i1NoSsKlMqqRIwKpQm1xHAjaZR9kjCVhZYl0qrx9z86Dx8T6+JxRykIBxd0cCxvGrrbYEjEcrAeMZajUKnqH3FjSE9INUQ0ieoxwYx1AOjONXW205MB6tHBjPUA6MZ+i9BTkwP0jlwHiOcmAcQzkwjl9tteXAeLRyYDxDOTCeofcW5MD8IJUD4znKgXEM5cA4frXVlgPj0cqB8QzlwHiG3luQA/ODVA6M5ygHxjGcEQ4MCxq+/fbbcbx48WK0HhjW3Lp06dKk+M9//tOEEE+ePGmwblkIfcnqw9q1a82bb74ZbB9PnDgRPMM1a9YEzRCLfOLneVnPQNPpeP7wHJYNV5Wt0GR5CNjBgwfjuGXLlkjAfvGLX0Q/CscPwxE3b94creCJVTybjqtWrTIrV65svB95HO69995o1di8Mk3miSH/HD/00EMGHJu8j3nnxqrFrVqR1YcQagjpg6IxGkLyHDWE5BjOiCFkEpEELEmk2rEErBo3t5YEzKVRfl8CVp5ZV2roU0gesz6F5BnqU0ieofcW5MD8IJUD4znKgXEM5cA4frXVlgPj0cqB8QzlwHiG3luQA/ODVA6M5ygHxjGUA+P41VZbDoxHKwfGM5QD4xl6b0EOzA9SOTCeoxwYx1AOjONXW205MB6tHBjPUA6MZ+i9BTkwP0jlwHiOcmAcQzkwjl9tteMXnWEAABKXSURBVOXAeLRyYDxDOTCeofcW5MD8IJUD4znKgXEM5cA4frXVlgPj0cqB8QzlwHiGcQv4Hx9/nTsZ8Be5R0ZGzLx586KYzE8ey4EliZQ/xhIr3/72t6O/LA3+IQYJGH9XJGA8Q4MXZHBw0PT29prh4eFJLSJv7ty5ZnR01Jw/fz4qO6lAyoEELAVKiaTvfve70XJEH/zgB6Ptpz/96ULcS5zCS1EJGI9RAsYzjFwXBAruKylgOE6mdTqlBKwToex8rJt27bXXRsJ11VVXxUJW9h5kn8FfjgSMZykB4xnGLaQJWF9fXyRsyNuzZ0+qE8CChlhZ0sadO3dGL96vf/1rs3r16jgifd++fUFETO5ipclQ+mP78ZWvfGWSeFkR+/znPx9cX9evXx8kQ8sS24ULF5q9e/cGx872cd26dQYc7XFoW7BrzYKGaQKGF2hoaChyYdj29PREQ8lY9YwxELDXX389jpggRz2swPrss8/G8bnnnjN///vfg4iPP/54tIJsKP2x/fjRj35krrnmmkkihuMf/OAHQXCz/cQWDA8dOhRcv9w+YsXTV199Ndg+Hj582ExMTATbv1deeSUyIO77XmS/kSWlswQME8o2YKjZaTijIaSlVX6Le2Bdl7t170H5VuupoSEkz1VDSJ5h3EKagGFi3/0UDJ9UDgwMxHXSdiRgaVSKp2Ee7Itf/GIkZF/4whdSPxku3lp9JSVgPFsJGM8wbiFNwJKT+P39/dEnknGllB0JWAqUCkn6ImsFaIkq+iJrAkjJw1Z9kTVNwOC+IFr4KgUi9jsFCVgnQsXyJWDFOOWVkoDl0emc1yoBy7scdxiZVw55ErBOhIrlS8CKccorJQHLo9M5b9oIWOdLfb+EBOx9FsyeBIyh915dCRjHUALG8auttn4LyaPVJD7PUJP4PEPvLciB+UEqB8ZzlAPjGMqBcfxqqy0HxqOVA+MZyoHxDL23IAfmB6kcGM9RDoxjKAfG8autthwYj1YOjGcoB8Yz9N6CHJgfpHJgPEc5MI6hHBjHr7bacmA8WjkwnqEcGM/QewtyYH6QyoHxHOXAOIZyYBy/2mrLgfFo5cB4hnJgPEO6BawH9vLLL8fx5MmT0UoKq1atihc5xGKHeOAvXrwYRDxw4EC0QGMo/Unrx4oVK8yFCxeC4JXWv/379wfPcPny5UEzxIKB4JjGN5Q0PIdlQyPrgZXtpC0PAcP/JDbihmAtq7vuuita1BALGyJCNI4cORJE3Lp1q9m4cWMQfclismjRomjRwKz8ptO3bNliNm3aFDzDpjnlnd++G3llmszDopWtWZHVChK71RwYS/C9+poD4zlqDoxjqDkwjl9ttTUHxqPVHBjPUHNgPEPvLciB+UEqB8ZzlAPjGMqBcfxqqy0HxqOVA+MZyoHxDL23IAfmB6kcGM9RDoxjKAfG8autthwYj1YOjGcoB8Yz9N6CHJgfpHJgPEc5MI6hHBjHr7bacmA8WjkwnqEcGM/QewtyYH6QyoHxHOXAOIZyYBy/2mrLgfFo5cB4hnJgPEPvLciB+UEqB8ZzlAPjGMqBcfxqqy0HxqOVA+MZyoHxDL23IAfmB6kcGM9RDoxj2HoHhr/IPX/+fNPb22t6enrMyMhIRyISsI6IChWQgBXClFtIApaLp2Nm6wVsYGDAjI6ORhcKMYOIHTt2LPfCJWC5eApnSsAKo8osKAHLRFMoo/UC1t/fb/Ai2YDj8fFxe5i6lYClYimdKAErjWxKBQnYFCSlElovYHBbcF1Lly6Nho9wZMmABQ0hajbiocGChj/96U/NfffdF8e1a9dGYogXs+mIRdqWLFnSeD/yOPzmN78xYJlXpsk8MeSf47GxsejdavI+5p0bz1+rFzR058BmzZoVvUxJAYNKuxHLS0PAnnjiCfPuu+9OileuXDEhRHyChqWvQ+hLVh/w8OA/h6z8ptPPnj1rTp06FWz/wGf9+vXR89c0q6zznzlzJlrJOCu/6XS8v3gOy4ZglpTu6+sz+F8C4fz589FkPhQ7L2gImUeneB444wEONehrFPyd0dcoeIa5LcBJuQET+sPDw27SlH0J2BQklRIkYJWwTaoE94DRQahBAlbzncH8l3VcdjhpHVnWqSVgWWTKpUvAyvFKKy0BS6NSPG1aTOLjk0cIGb4L1sl9AY0ErPgDkldSApZHp1ieBKwYp6xSrRewrAvLS5eA5dEpnicBK84qq6QELItMsXQJWDFOXS+l30LyyDWJzzPUHBjP0HsLcmB+kMqB8RzlwDiGcmAcv9pqy4HxaOXAeIZyYDxD7y3IgflBKgfGc5QD4xjKgXH8aqstB8ajlQPjGcqB8Qy9tyAH5gepHBjPUQ6MYygHxvGrrbYcGI9WDoxnKAfGM/TeghyYH6ShO7Bly5ZFKyn4udp6WpED47jKgXH8aqstB1YdLZZY+tSnPhWtOILfyn7yk5/suMhl9bNxNSVgHD8JGMevttoSsOpob7755li8IGCIn/nMZ6o3WGNNCRgHd0YIGNaswnyIjQcOHIge6t/+9rdm27ZtcTx06JA5evRoEHH79u1m06ZNQfQli8nixYvNk08+GVQft2zZMkW8rIghL+tamkpftGhRcH1yWYAZ3hE3LbT9Vi9oWES/IWAvvvhiHE+cOBE95CtWrDBHjhyJIxbAw5piIcR9+/aZ3bt3B9GXLB7Lly83zzzzTFB9tPfWipa7RV7WtTSVjnm6Z599Nrh+WR579uwxiPY4tC2ePzyHZcPkRbjK1m64vCbx/dyAUCfxv/a1r5nrrrsudmIf+tCHzJe+9CU/F+25FQ0hOaAzYgiZRCQBSxKpdhyqgGFduG9+85uxgH396183SAsxSMC4uyIB4/jVVluT+DxafQ+MZ6jvgfEMvbcgB+YHaagOzF6dBMySqL6VgFVnV1tNCZgftBIwnqOGkBxDDSE5frXV1hCSRysHxjOUA+MZem9BDswPUjkwnqMcGMdQDozjV1ttOTAerRwYz1AOjGfovQU5MD9I5cA4jvhqx+23325ef/11rqEaa0vAaoRbtWkJWFVyk+tJwCbzKHOEP//n/kpgZGSkTPWulZWAdQ118RNJwIqzyispAcujk50Hbq542X2khxYkYKHdkZb8YduJiQmDH52HHFatWmXwO9NQAxg+9thjwXXve9/7XqqA3XrrrcH19eDBg+bw4cPB9ct26N133zUPPfSQPSy81W8hC6OqVhDitXPnzmqVu1Rr4cKFQQuY/UF8l3AUPs3Q0JD5wAc+MEXEkB5KwPzcggULzPXXXx9F7Hfz51g4V5HzQcDwHJYNErCyxEqWl4CVBJZSPFQBGx8fnyJeGEYiPZSA35LiR/B2eHvNNdeYW265pavdGxgYMPPnz49W1c0SMwlYV29J8ZNJwIqzyioZqoChv2NjY+aGG26IBAJbHIcSIBZWuJLbLCGpq+/f+c534r584xvfmCJm01LAsMZSXrznnnsiKPgIO69ck3k/+9nPzI9//ONg+wc23//+96MHqklOeee+7bbbzE9+8pOgGQ4ODhosyJd3Hd3O++UvfxmLRlLA7rzzzq73FUsh2X5ce+210b4Vs0uXLk2/IeS3vvUt8/GPfzwzzp4929x4443mIx/5SGaZvPrdyEMfZ82aFWz/wOCjH/2o+djHPhZsH9vCsBvPU9lzXH311bFoWPHAvF3ZdnyUx3tg+4Ct7RueP3wgsnr16tIGUHNgpZGVq3Dx4kXz1FNPlavU5dJYqfPKlStdPmvx0124cCFaMbZ4je6XxKq7+DlMaAFDWlc0PvzhDzfyh1HwB1pgNmxf0A/MjdmvnOD5qzJ3KAGr+YmTgPGAJWAcQywfjU/48HWZbs99oecQL7hozBG6ouVe1bQTMKgxvuUM4Ph285w5c6KIj4FtaMMXWSVg9m5V30rAqrOzNe3fPLDH3dpCPPG1Euu0ss47rQQMwgXri4vv7++P/9ewdth+0iMBy3ocyqXv379fQ8hyyKaUBsMQh5C2o00JmD1/py0EDAzLhuCGkKOjowYRobe3NxIx96KQ1tfXFyW1QcDcvmtfBETAL4GgBAxjZQgUAlxW2jea4c4kYH4fArUmAm0lEJSAYbhoh4dZQCVgWWSULgIzj0BQAoaPWDt9lIpPMawza8MQEh9CwFmGGtA3+wdPQ+wj5kHtH2UNsX9un/Cfb6fn1y3fjX08f5af3TbxSWSRa7XPYpn3JRgBQ6chYJ3g9vT0xPNiELAf/vCH0Z9LLwKo22XwMOPLe3bI2+3z550PnNEv/IcAVwuundxvXnt15KFfmFLAFv1EHzs9H3X0o0ib9l6jryEF9Avc0C8b8Z9CSAH3dN68edHziD6WeQ6DE7C8/8FwYdZ9hXQD0vqChwQvHz4+DlHA0Gf3QcY+HvSQQlKscO/tBzyh9RP3Gv0LUcBCf2fwn1PV+xqMgOGBhAPDxaQFvGAQguRDnVY2pDQIcqgC5nIC19AEzO0f9sGxzP/Oyfp1HWPuFv9RWYdT13mqtAthCE1Uk9eB975qqF6z6hlz6kG8cDHJhxQigP9F2iZeuNS2CFiIL5/lhy8yQyRCdBIQLtuvEBlCwOw0BrbuF8FzXsWuZdn3Awxxj+2opWgHghIwCJQVsblz50bjYhwnBa3oxYVQzt6gEPqS1QfwxYMTYgA/CAMecPSxzARv3ddjpwnsf6whCpjLAP2ESFQdrrlt+drH/YWw2vuKPuLYnd7IO1dQAuZ2FBdmHww3vW37oQuYFa82sEZf8QKGEtAXLNQHh4iIiWjEkP/DDe15TOsPpgqQXiQEK2BFOt+GMmk3KJR+t0m8wCw0AYNrwP21EaMFROsmQrnPbj+sm3XTmtzHf5xJ949jCViTd8U5d6gChpcM842YE7EOAtui1t25xNp2IQZLly6NvseELVY0CF0cIBAhBTC09xiLLob4VRQwg5PF99TwDJb50EsOrOanDf/DhPjSQajsnI27DUnAIP6h9i3tsQG7kPihj3j+wBHutairSbu2utPsvS47PycBq/vOqH0REIHaCEjAakOrhkVABOomIAGrm7DaFwERqI2ABKw2tGpYBESgbgISsLoJq30REIHaCEjAakOrhkVABOomIAGrm7DaFwERqI2ABKw2tGpYBESgbgISsLoJq30REIHaCEjAakOrhkVABOomIAGrm7DaD54AfsbCLKoX/AVO4w5KwKbxzc27tJCXfMnrdx15ErA6qHanTQlYdzgHdRb8wFeO4/1bIgF7n0Xb9iRgbbtjZH+xWgIW3YOA2QX47GoZEDYsuWJXw026NCxzYsvMmTMnXrgP6WgDS6IgHVscQxiwj/ZsWlb3seIqymP1CZRHxDIwOJ8NKGP7atPQR6TbYNvBdaAvuEYs+4zrdq8N57LBCpi9Btvf5MoS6Iu9HrTrtoG2sMCh5RP60j/22tu+lYC1/Q6W7D9eMCxZAgHDC4hoRQILydkF+fDSY+0oV8Ss6KG+Ww/pEDHUgQigDYiHTUNZpEEYsgLK4qWHgFnxw/lxbAPKoC03IB/pNmDf9htl7bUiHf1DGurgXPa6kWavAfvuNdh2UdbtH9rC0scob4NtI8nH5mvrn4AEzD/T4Fu0L6zbUStYbhrEyxUdvKCuoNiySHeFDs4FaWjThrRz2jxsITCuECEtTZxcwcgqA7F0A4TGdWnIQ/9sW7ZvScdlhRDlIUrJlUPRprvEdZKD2wft10NAAlYP16BbtS+s20mIBVyTuzorhlx4KW1wX3qbhm1aOtKSguC25dbHPsQrKY7opytq2LeiY+uniVyyHdRzxTTZ5zQeyT5BqDBsdPng2O1f2jXbfmpbD4H3n8562lerARJIe2Hx0tu1yJHvRnsJaUKFvLT0NLFKS7NtQwiSwoM+uAKBfaS5oaiAJeu5fUZeWt8gWrZPODecHcq6EcNNG9LasHna1kNAAlYP16BbTXthMURyh4tpF+C+9G5+Wnray5yWZtspKmDopxsgKkmRs6Jjy6UJn9tny8POidl6EHTbFrbucNGWcbd51+eW074/AhIwfyxb05Kdo3KHeHh5MVeEIZINSEs6DLzsyeCKgc1Le5nT0mz5IgIGAcGngDagb5hY9yVgGDLbgDk99NcysszcuT7wsfmol3d9tl1t/RKQgPnl2ZrW4Fzw8rtfB4AgwHXgRcR8GLbuhDiOmxQwiAUm1tFv9M86JB8ChjYwKQ8RR9vYJufNcIx0nB8RPFxBw7FCdwmIeHd5B3W2pMOynUN6mlDZ/Ka3EDLX+fjsTxYT9xyh83H7Ot33JWDT/Q7r+kRgGhOQgE3jm6tLE4HpTkACNt3vsK5PBKYxAQnYNL65ujQRmO4EJGDT/Q7r+kRgGhP4P0lsFwtiUIPyAAAAAElFTkSuQmCC[/img][br][br]Is this sequence arithmetic or geometric? Explain how you know.
List at least the first five terms of the sequence.[br]
Write a recursive definition of the sequence.[br]