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: 40


The common ratio is -3 so yes, this is a geometric sequence. The explicit formula is $a_{n}$=3$\times$ $(-3)^{n-1}$. The recursive formula is $a_{1}$=3;$a_{n}$=$a_{n-1}$ $\times$ -3

Work Step by Step

You are given the sequence 3,-9,27,-81.The starting value $a_{1}$=3.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=$\frac{-9}{3}$=-3 r=$\frac{-81}{27}$=-3 There is a common ratio, r=-3. So the sequence is geometric. Substitute a1 and R into the explicit formula($a_{n}$=$a_{1}$ $\times$$r^{n-1}$).The explicit formula is $a_{n}$=3$\times$ $(-3)^{n-1}$. Substitute a1 and r into the recursive formula ($a_{1}$=A;$a_{n}$=$a_{n-1}$$\times$R). The recursive formula is $a_{1}$=3; $a_{n}$=$a_{n-1}$ $\times$ -3
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