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: 26

Answer

The $n^{th}$ term of the sequence is given by the formula: $a_n =0 \ (\dfrac{1}{\pi})^{n-1}=0$ and $a_5=0$

Work Step by Step

The general formula for nth term $a_n$ of a geometric sequence is: $a_n=a_1 r^{n-1}$ We are given: $a_{1}=0 ; \ r=\dfrac{1}{\pi}$ Therefore, the $n^{th}$ term of the sequence is given by the formula: $a_n =0 \ (\dfrac{1}{\pi})^{n-1}=0$ Now, the 5th term can be computed by substituting $5$ for $n$: $a_5=0 \ (\dfrac{1}{2})^{n-1}=0$
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