Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 9 - Sequences and Series - 9-3 Geometric Sequences - Practice and Problem-Solving Exercises - Page 584: 24



Work Step by Step

Recall the formula for the $n^{\text{th}}$ term of a geometric sequence: $a_{n}=$ $a_{1}$ $\times$ $r^{n-1}$ where $a_n$ = $n^{\text{th}}$ term; $a_1$ = first term; $n$ = term number' $r$ = common ratio The given geometric sequence has: $a_{1}=-30$ , $n=8$ and $r=\dfrac{7.5}{-30}=-0.25$: Substituting these values into the formula above gives: $a_{8}=$ $-30$ $\times$ $(-0.25)^{8-1}$ $a_{8}=$ $-30$ $\times$ $(-0.25)^{7}$ $a_{8}=0.0018310546875$ The $8^{\text{th}}$ term is $0.0018310546875$.
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