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: 34


The recursive formula is $a_{1}$=260 and $a_{n}$=$a_{n-1}$ $\times$ $\frac{1}{2}$.

Work Step by Step

Use the recursive formula $a_{1}$=a, $a_{n}$=$a_{n-1}$$\times$r. The starting value is 260 so it is the $a_{1}$ You have the sequence 260,130 so use the common ratio formula(r=$\frac{{a_{2}}}{{a_{1}}}$) r=$\frac{130}{260}$=$\frac{1}{2}$ .So the common ratio is $\frac{1}{2}$.Substitute the value of a1 and R into the recursive formula: The recursive formula is $a_{1}$=260 and $a_{n}$=$a_{n-1}$ $\times$ $\frac{1}{2}$.
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