Situations and Sequence Types: IM Alg2.1.10
[url=https://im.kendallhunt.com/HS/teachers/3/1/10/preparation.html]“Situations and Sequence Types”[/url] from IM Algebra II © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg2.1.10 Lesson
- IM Alg2.1.10 Lesson: Situations and Sequence Types
- Alg2.1.10 Practice
- IM Alg2.1.10 Practice: Situations and Sequence Types
IM Alg2.1.10 Lesson: Situations and Sequence Types
Here is a geometric sequence:
16, 24, 36, 54, 81[br][br]What is the growth factor?
One way to describe its growth is to say it’s growing by ____% each time. What number goes in the blank for the sequence 16, 24, 36, 54, 81?[br] Be prepared to explain your reasoning.[br]
The table shows two animal populations growing over time.
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[/img][br][br]Are the sequences represented by Population [math]A[/math] and Population [math]B[/math] arithmetic or geometric? [br]Explain how you know.
Write an equation to define Population [math]A[/math].[br]
Write an equation to define Population [math]B[/math].[br]
Does Population [math]B[/math] ever overtake Population [math]A[/math]? If so, when? Explain how you know.[br]
Define the sequence W so that W(n) is the number of white squares in Step n, and define the sequence B so that B(n) is the number of black squares in Step n.
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWwAAAB4CAYAAADWr8iAAAATHklEQVR4Ae2dwaocxRvF70ZRFKIbQRBuQEQEMXHhSjRZuY1vkLxBXAqC+gYGfACzcK8L9+YN8gh5hPgCMn9+k/8HZaW6q/s7PdPT6VPQzExXnarq853vdE3fe+teHVzMgBkwA2ZgEwxcbWKWnqQZMANmwAwcbNgWgRkwA2ZgIwzYsDcSKE/TDJgBM2DDtgbMgBkwAxthwIa9kUB5mmbgXAz89NNPh6urKx8rcfD3338PhtqGPUiNK8zAPhm4c+fO0ax5zRyY/Y0bN1LYW7duHce+vr5eBc+4zJ95ZK5dxcMb4w+V4ZohhM+bATPwSjMQhp29SAyHPjKF1SV4VvmZouLj28XYKndsXiq+x70Ne4x915mBHTLQM40eJTbsq0PW8Hvc27B76nO9GdgZAz3T6NFhw7Zh9zTiejNgBhZiwIadN1w/EllIhO7GDJiBaQzYsG3Y05TiVmbADKzOgA3bhr26CD0BM2AGpjFgw7ZhT1OKW5kBM7A6AzZsG/bqIvQEzIAZmMaADduGPU0pbmUGzMDqDNiwbdiri9ATMANmYBoDNmwb9jSluJUZMAOrM2DDtmGvLkJPwAyYgWkM2LBt2NOU4lZmwAyszsAShv3ll18e/vnnn9nHX3/9ddz86fvvv5+NZTwVz7j8aT39ZOYfeO8lsrqM9zWBhw8fHoWLeH3M5+DBgweH58+fb1I0YdiO+/y4L8XZkHC8+dMQMzs/H0nLa+aIfX0z2Bg7u6eyilf3ZI49kbOrrLWlF/xlYvf111/7Bn91dfj444+lvBnSgA17iJmdn4+kzdKg4lmp0Ee2KHiMFnx2T2Z1A6DsNS+FU2L377//2rCvrg6PHz9OhaPHvQ07ReurD+oJp8eAilcMl7kpeBv2i/8404txq96G/eIxig27pQ6fOxkDquGqeMVwIUXB27Bt2OhHOWzYJ7Mmd9xiQDVcFa8Yrg27FdHp55TYeYXtFfZ0pbnlYgwoScskVLwNe7FQzu5IiZ0N24Y9W3AG6AwoScvoKt6Grccw24MSOxu2DTurO+MEBpSkZVgVb8MWgidCldjZsG3YovwMzzCgJC3jqXgbdiZqy2CU2NmwbdjLqNC9zGJASVoGUvE27FnhWrSxEjsbtg17UTG6s2kMKEnLCCrehj0tTqdopcTOhm3DPoUm3WeHASVp6VrF27A7ATphtRI7G7YN+4TSdNdDDChJS58q3oY9FJnTn1diZ8O2YZ9eoR7hJQaUpKUzFW/DfikkZzuhxM6GvbJhP3369PDkyZNdHlz7XkskbTb2n3322fFPe3///fdD5sCwP/nkkxSW8RT8Dz/8cMSzRWrm+sEx/tZ368tce/xZP9e/54N9sTP83b59+8jbkO+Mbv707NmzQ3SwR/K59r2adhj2HuO+1DVv3bCX4sH9zL95pQw7tom8f//+catJPs85Yl/gOZiyrYpHKPRR9jnnPXiMa48lDHsOX2Xb1157bfMrrJs3b6a0E9xt3bDLeE59/+OPP24+7kvcYO7du5fSTnjekOeMrrAJEpPPCi+EOzR477yKVw1Xxfeu75LrVe7feuutzSfu3bt3UyFS8yY16IIgJfZ+hr3iM2xVeErg0Z+KVw1XxS+YQ2fvSuXehp1f6Jw92NWASuxt2DbsSk7TP6qGq+Knz/TyWipJy9XYsG3Y5M9ej1X2w/YK28+ws7cSG7YNe69mzXXbsBPOAXGsFLNFxWfHvQScV9hXBz/Dnq9EPxLxI5H5qvk/QjVcFZ+e+AUAbdg27IwMbdg27IxujhjVcFV8euIXALRh27AzMrRh27AzujliVMNV8emJXwDQhm3DzsjQhm3DzujmiFENV8WnJ34BQBu2DTsjQxu2DTujmyNGNVwVn574BQBt2DbsjAxt2DbsjG6OGNVwVXx64hcAtGHbsDMytGHbsDO6OWJUw1Xx6YlfANCGbcPOyNCGbcPO6OaIUQ1XxacnfgFAG7YNOyNDG/YFGPajR4+kvV1//fXXQ+b46KOPjn/amsGCwXA//fTT1NzZy9aGfZXm7o033tj8nyV//vnnqev3ftgvTIv82euxyn7Y8afpeyXdhr3fhFtC89ldLjMr2yUx8e1qCQ7cRy6HhuI5aXvV7H7Yl7CfxOuvv57alzZuVoh3jyWSFh4yh/fD3v5eIpm4ez/sFwa9yf2w33vvvdW/Er399ttpv/UKe/R+PsrrJdys1dWd9xIZDXGz0s+wXxj2Jjd/smE3Nb2Jk7HCzk7Whr39FXYm9jZsG7a0SvcKO5N2+j+PsGHbsNVvOFvGe4Wd/ImzDduGnU18PxKZrx2vsL3C9gp7ft7ICD8S8e9hZ0Rkw7Zh27AzmSNibNg27IyEbNg2bBt2JnNEjA3bhp2RkA3bhm3DzmSOiLFh27AzErJh27Bt2JnMETE2bBt2RkI2bBu2DTuTOSLGhm3DzkjIhm3DtmFnMkfE2LBt2BkJ2bBt2DbsTOaIGBu2DTsjIRu2DduGnckcEWPDtmFnJGTDvgDDzu6H/e6770pmm/0LtRL35ptvpvY09n7Yd46xg4fM4f2wt/+n6Zm4s6VsmX97fe/9sJN/mq4KhpXmHkussFX+9oz3ftgvVpt71kD22oc8Z3T/zNgTOrsf9gcffHC8237zzTeHzBEr9AwWDGS9//77qf2c49r3btiZPZHBwDv8K7Ej/mvgv/jii+Pcv/rqq5R24ma3dcPOxp64Z2MX3H/44Yep2Kt4xmX+9JPRXuCznnl9fX0cXzLsrPBCuEOD986reIhXDFfF967vkutV7lW8yr2Cj6/1GFamgGP8bN5kxlwSs2bsVO5VvBo7Fd/jftIKOyu83uA9kal4JWmZm4rvXd8l16vcq3iVewW/dtKvrYs1Y6dyr+JVw1XxPe5t2CPZoST9SLebqOoJp3cRKl7lXsGvnfQ9bk9dv2bsVO5VvGq4Kr7HvQ17RP1K0o90u4mqnnB6F6HiVe4V/NpJ3+P21PVrxk7lXsWrhqvie9zbsEfUryT9SLebqOoJp3cRKl7lXsGvnfQ9bk9dv2bsVO5VvGq4Kr7HvQ17RP1K0o90u4mqnnB6F6HiVe4V/NpJ3+P21PVrxk7lXsWrhqvie9zbsEfUryT9SLebqOoJp3cRKl7lXsGvnfQ9bk9dv2bsVO5VvGq4Kr7HvQ17RP1K0o90u4mqnnB6F6HiVe4V/NpJ3+P21PVrxk7lXsWrhqvie9zbsEfUryT9SLebqOoJp3cRKl7lXsGvnfQ9bk9dv2bsVO5VvGq4Kr7HvQ17RP1K0o90u4mqnnB6F6HiVe4V/NpJ3+P21PVrxk7lXsWrhqvie9zbsEfUryT9SLebqOoJp3cRKl7lXsGvnfQ9bk9dv2bsVO5VvGq4Kr7HvQ17RP1K0o90u4mqnnB6F6HiVe4V/NpJ3+P21PVrxk7lXsWrhqvie9zbsEfUryT9SLebqOoJp3cRKl7lXsGvnfQ9bk9dv2bsVO5VvGq4Kr7H/STDfvDgweHnn3+efdy8efO4H0cGC0bFk7T0kR1fSfpTJ9Wp+w/hZLm7hNhlY4/eif3du3dT2gEHHvPYYlFjr+Sdyr2Kj9hlPU/FR94M6WaSYROAvR6Id48lknavcV/iurdu2Etw4D5y3jnkOaOGDejp06fHlQLi29vBte+1PHv2bHfxXlLf8LfV4tiv63XPnz8flE7XsAeRrjADZsAMmIGzMmDDPivdHswMmAEzkGfAhp3nzkgzYAbMwFkZsGGflW4PZgbMgBnIM2DDznNnpBkwA2bgrAzYsM9KtwczA2bADOQZsGHnuTPSDJgBM3BWBmzYZ6Xbg5kBM2AG8gzYsPPcGWkGzIAZOCsDNuyz0u3BzIAZMAN5BmzYee6MNANmwAyclYG0Yf/222/H3cxu3759fGWXqkePHh22socC8/z2228PDx8+PCvhexmMfTngF12ERr777rvDn3/+edEUoAvmWc6bHQvH9ne46Au6oMnBLbvgwW0cfL50TbCnUK0J5r2G1802bIRLArIL161btw73798/sLMb7zn3yy+//Ecif/zxx8VtM8mc3nnnneN897ob33+CtPCH2BP4+vr6cO/eveMRu/+hk7Igem7+l1DQLhq+cePGUddcB/PnHJq3aeejRIyDW7QQvgHXHGWBZ26Sl1BCE2iZOaMJXpkz13PuDeJmG3ZcQCvJSL5a1CQoF3kpJcwE0pmbDXvZyCBghIzR1QVt1KsS4nEpMeBbAd+4ag2H5nl1yTGAwZFvNbf0VpseCyo0dAmFubXiznmu6dzanc0KE5xKZiRvz7BJ4idPnhyPVkDrwNFmTvvAx3wiAFzHuQmPubyqr7GSwvx6hTiycp0SA/oj5rXhD40xt/1QP3F+6CYU9X4dZoBYwF/PB6KH+FYTn4deI8bk9ZRCOzQ0tX2vzzle2Otrav1sw2ZlCvk9Y412tC2PMmj0wXPOsp5HFa3VO20wWlZAZXvez/n6VCY82ClmMZVMtzscH3/BayuGJT8kTTyWKuNZx4N+6nZoptYfOI7ycVf0y/PSun05lynv6av1rWEKdu9tyDn46/28aEgTYMsyNcZ4Df/BhX7jP7mEJlgoqMbNNwYelZyz/JeJCSPHCoqH7mNJABkYLARh3twNOUrDJMH4WkE7zoOJuytty0I/JC4kETDa04bP1MWqucT03oOrDaKHcf04A2iCmEaiDLWmXcSPGPKeo0yi0Br64TwxLzVV9k0c0QcJRBvac5C0xBnTzhb6yWosO+arhiMuxIcYD5VSE/AdmigxvI+85T0YdILm6hhH7BmX97QvNYRGwWdKaJN+z1lmGzaTi9UzRPDTU0holSC3dVHxnKpltAQXMstCkDhaY4UYyvZT3kfgp7R1m+kMEFsSCH65saODoYLRtm6aJBL6atVFImKkUWjHeC09hV6ZV6bQN9eTTe7MmK8ahliFJjDWx48fD15ixLLVIFa1dSzCQHmNEjoh/nWJ9i291G35TPv4/6aszrmWlq+1sEueSxk2EyAJg1gSha+ptZmOGXYkUU08fUddeaFj5hqPScaMoewr3o/1GW38mmMALUQc4ZkbcMsw0RBHXUI7ZQJGm1ZdaLGlp1ghZxKMhGb+rXnEfPw6jQFiQwzCuNEEvwpcl4hlfR5NEYvWo5WoK2PMe9q3fIG5UNfSXj0un2NOYDi46bTm3sIueS5t2DEJkiESs/7KE4lVkhi4IIALrw8CWRPN56FniHG3bAUmxmu90ufUgLXwPtdngMTA9PgWBN+1FuC/FYNINlYztT44V/cVehqaUSbWoSv07bIcA2gCbkMTfAsry1Asw0/wh1oTfK5jHBoqv4mV4zB+S3tlm9Z7bg7RN+Oes8iGHZONVUxpqkFwnaRgICqeLVHfOiAmCsEYSpwYx4YdbF3eK0kaP28o44oOWkkTCUHMW9rgXBlv+kAjQ6VO5qF2cd5mHUyc9jV+ZlWa6lAsI8/BDGmCuEUJDZV6izpeh7RXthl7n/1mP9Znr25Y4T1ko74mOgiGuLrUbev6+vNYwkVgygSu8a3PY3222vucxkCYYBmnoaSJRxGtxyitWYzpKb7+Dt3w6/5inlPb13h/ns5AyyOGYtlqOzZSzxfU/I/5TH0OPjbXqXWLGzbPp6LEBbUMOxKSNlMK5LIib5UI8NCdtIXhnBqwoX59vs1AK+ZDhh3f2KaaZmigpacw4CmJFW2njtu+Up+dykB4RBmbiGWrD/xl6mOIMOyy7+gzxm09D482vdeWnnsYtX62YQ+teIaEjim2xI+5Qj7Po8qvQ3FB9Tn64ah/5zrGLR/FRB+9Vxt2j6H59cSNFW1diDc33PKGThuSk/MtTCRuS3P1zTna8ny77Iv3aIxxy/P1/PgcWmrptdXe56YxgCbqeIEkHvHziLI+jLY8FyPFY4jaB6infRnj6If4l32V49Y+E+PEK5poFfoLPZdjttoueW62YYdxlg/9ISTMr558PKOiPSSXBJCIJBIXXvbHZxKwLPRPX7QnyPygAgznOVcGpMSNvY85j7Vx3TwGIkmIURnTiFOdIGGSaAh9lD+AQkvx3LvsL/RWzgy9cJ72vPJbSxxoibFL3ZW48j3tekdrBV/24fcvMxCaIC4tTdSxQSPEgdjxa8O1Jsqbc/QXxl/GJ8blBhweQ1+hnymr69AD44Dl4D3n8Z1azy9f/bJnZhs2JsuFQlocfC6JKqdI0kFctK1XSxhtq7+aCAiin7o92PomUY4/9p7+arGMtXddnwHiw1fFiDevJAznhuKEJrgZR9t6FGIU9dGm1hHn0QilHJ+xh7RZj4MeekdmYVCPs7fPoYkyhrwf0wQxi/a81qXWBG04V2qMWIYmyva0rfVT9x+f8SH6QV9xgB+be2BP8TrbsE8xiSl9hmFPaes2+2OgNOz9Xb2vuMVAadit+i2es2FvMWqe80sM2LBfomT3J2zYK0rAK+wVyd/A0DbsDQTpzFO0YZ+Z8HI4G3bJht/XDNiwa0b82YZtDZgBM2AGzMBqDGzmGfZqDHlgM2AGzMCFMGDDvpBAeBpmwAyYgR4D/wOMwvGGY6cPpwAAAABJRU5ErkJggg==[/img][br][br]Are the sequences [math]W[/math] and [math]B[/math] arithmetic, geometric, or neither? Explain how you know.
Write an equation for sequence [math]W[/math].[br]
Write an equation for sequence [math]B[/math].[br]
Is the number of black squares ever larger than the number of white squares? Explain how you know.[br]
A definition for the [math]n^{th}[/math] term of the Fibonacci sequence is surprisingly complicated. Humans have been interested in this sequence for a long time—it is named after an Italian mathematician who lived from around 1175 to 1250. The first person known to have stated the [math]n^{th}[/math][sup][/sup] term definition, though, was Abraham de Moivre, a French mathematician who lived from 1667 to 1754. So, this definition was unknown for hundreds of years! Here it is:[br][math]F\left(n\right)=\frac{1}{\sqrt{5}}\left(\left(\frac{1+\sqrt{5}}{2}\right)^n-\left(\frac{1-\sqrt{5}}{2}\right)^n\right)[/math][br][br]Which form (recursive or [math]n^{th}[/math] term) is more convenient to use for finding [math]F\left(5\right)[/math]?
What about [math]F\left(10\right)[/math]?
What about [math]F\left(100\right)[/math]?
What are some advantages and disadvantages of each form?
IM Alg2.1.10 Practice: Situations and Sequence Types
[size=150]A sequence is defined by [math]f\left(0\right)=3[/math], [math]f\left(n\right)=2\cdot f\left(n-1\right)[/math] for [math]n\ge1[/math]. Write a definition for the [math]n^{th}[/math] term of [math]f[/math].[/size]
A geometric sequence, [math]g(n)[/math] starts 20, 60, . . . Define [math]g[/math] recursively and for the [math]n^{th}[/math] term.
A geometric sequence g starts at 500 and has a growth factor of 0.6. Sketch a graph of g showing the first 5 terms.
An arithmetic sequence has [math]a\left(1\right)=4[/math] and [math]a\left(2\right)=16[/math]. Explain or show how to find the value of [math]a\left(15\right)[/math].
An geometric sequence has [math]g\left(0\right)=4[/math] and [math]g\left(1\right)=16[/math]. Explain or show how to find the value of [math]g\left(15\right)[/math].
A piece of paper has an area of 96 square inches.
Complete the table with the area of the piece of paper [math]A\left(n\right)[/math], in square inches, after it is folded in half [math]n[/math] times.
Define [math]A[/math] for the [math]n^{th}[/math] term.[br]
What is a reasonable domain for the function [math]A[/math]? Explain how you know.[br]
Here is a growing pattern:
Describe how the number of dots increases from Stage 1 to Stage 3.
Write a definition for sequence [math]D[/math], so that [math]D\left(n\right)[/math] is the number of dots in Stage [math]n[/math].[br]
Is [math]D[/math] a geometric sequence, an arithmetic sequence, or neither? Explain how you know.[br]
A paper clip weighs 0.5 grams and an empty envelope weighs 6.75 grams.
Han adds paper clips one at a time to an empty envelope. Complete the table with the weight of the envelope [math]w\left(n\right)[/math], in grams, after [math]n[/math] paper clips have been added.[br]
Does [math]w\left(10.25\right)[/math] make sense? Explain how you know.[br]