Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.3 Geometric Sequences; Geometric Series - 11.3 Assess Your Understanding - Page 844: 22

Answer

The $n^{th}$ term of the sequence is given by the formula: $a_n =6 \ (-2)^{n-1}$ and $a_5=96$

Work Step by Step

We are given: $a_{1}=6 ; \ r=-2$ The $n^{th}$ term of the sequence is given by the formula: $a_n=a_1r^{n-1}$ $a_n =6 \ (-2)^{n-1}$ Now, the 5th term can be computed by substituting $5$ for $n$: $a_5=6 \ (-2)^{5-1} \\ =6 \ (-2)^4 \\=96$
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