Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-8 Geometric Sequences - Practice and Problem-Solving Exercises - Page 470: 31


The recursive formula is $a_{1}$=2 and $a_{n}$=$a_{n-1}$ $\times$ -4.

Work Step by Step

Use the recursive formula $a_{1}$=a, $a_{n}$=$a_{n-1}$$\times$r. The starting value is 2 so it is the $a_{1}$ You have the sequence 2,-8,32 so use the common ratio formula(r=$\frac{{a_{2}}}{{a_{1}}}$) r=$\frac{-8}{2}$=-4 and r=$\frac{32}{-8}$=-4.So the common ratio is -4.Substitute the value of a1 and R into the recursive formula: The recursive formula is $a_{1}$=2 and $a_{n}$=$a_{n-1}$ $\times$ -4.
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