[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.
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].
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]
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]
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]