College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.3 - Geometric Sequences; Geometric Series - 9.3 Assess Your Understanding: 19

Answer

$a_5=162$ $a_n=2 \cdot 3^{n-1}$

Work Step by Step

RECALL: The $n^{th}$ term $a_n$ of a geometric sequence is given by the formula: $a_n=a_1 \cdot r^{n-1}$ where $a_1$ = first term $r$ = common ratio The given geometric sequence has: $a_1=2$ $r=3$ Thus, the $n^{th}$ term of the sequence is given by the formula: $a_n = 2 \cdot 3^{n-1}$ The 5th term can be found by substituting $5$ for $n$: $a_5=2 \cdot 3^{5-1} \\a_5=2 \cdot 3^4 \\a_5 = 2(81) \\a_5 = 162$
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