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 471: 35


The explicit formula is $a_{n}$=48 $\times$ ($\frac{3}{4}$$)^{n-1}$ The recursive formula is $a_{1}$=48 and $a_{n}$=$a_{n-1}$ $\times$ $\frac{3}{4}$.

Work Step by Step

The starting value is 48 so it is the $a_{1}$. You have the sequence 48,36 so use the common ratio formula(r=$\frac{{a_{2}}}{{a_{1}}}$) r=$\frac{36}{48}$=$\frac{3}{4}$.So the common ratio is $\frac{3}{4}$.Substitute the value of a1 and R into the explicit and recursive formula: The explicit formula is $a_{n}$=$a_{1}$ $\times$ (r$)^{n-1}$ so the explicit formula is $a_{n}$=48 $\times$ ($\frac{3}{4}$$)^{n-1}$. Use the recursive formula $a_{1}$=a, $a_{n}$=$a_{n-1}$$\times$r so the recursive formula is $a_{1}$=48 and $a_{n}$=$a_{n-1}$ $\times$ $\frac{3}{4}$.
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