## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 7 - Exponents and Exponential Functions - 7-8 Geometric Sequences - Practice and Problem-Solving Exercises - Page 471: 41

#### Answer

The common ratio is $\frac{1}{7}$ so yes, this is a geometric sequence. The explicit formula is $a_{n}$=98$\times$ $({\frac{1}{7}})^{n-1}$. The recursive formula is $a_{1}$=98;$a_{n}$=$a_{n-1}$ $\times$ ($\frac{1}{7}$)

#### Work Step by Step

You are given the sequence 98,14,2,$\frac{2}{7}$.The starting value $a_{1}$=98.Find the common ratio by using the formula: R=$\frac{a2}{a1}$,R=$\frac{a4}{a3}$.Plug in the values to get the ratio: r=$\frac{14}{98}$=$\frac{1}{7}$ r=$\frac{{\frac{2}{7}}}{2}$=$\frac{1}{7}$ There is a common ratio, r=$\frac{1}{7}$. So the sequence is geometric. Substitute a1 and R into the explicit formula($a_{n}$=$a_{1}$ $\times$ $r^{n-1}$).The explicit formula is $a_{n}$=98$\times$ ${\frac{1}{7}}^{n-1}$. Substitute a1 and r into the recursive formula ($a_{1}$=A;$a_{n}$=$a_{n-1}$$\times$R). The recursive formula is $a_{1}$=98;$a_{n}$=$a_{n-1}$ $\times$ $\frac{1}{7}$

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