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 11.2 Arithmetic Sequences - 11.2 Assess Your Understanding - Page 834: 20


$a_n=\dfrac{4-n}{3}$ and $a_{51} = \dfrac{-47}{3}$

Work Step by Step

The $n^{th}$ term of an arithmetic sequence is given by the formula: $a_n = a_1 + (n-1)d (1)$ where $a_1 = \ First \ Term; \\ d = \ Common \ Difference$ We have: $a_1=1 \\ d=\dfrac{-1}{3}$ Next, we will substitute the above data into formula (1) to obtain: $a_n=1+(\dfrac{-1}{3})(n-1) \\ a_n=\dfrac{4}{3}-\dfrac{n}{3} \implies a_n=\dfrac{4-n}{3}$ In order to compute the $51st$ term, we need to plug in $51$ for $n$ into the above form to obtain: $a_{51} = \dfrac{4-51}{3}$ So, $a_{51} = \dfrac{-47}{3}$
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