Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 22


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

Work Step by Step

We know that the $n^{th}$ term of an aritihmetic sequence is given by the formula $a_n=a_1+(n-1)d$ where $d$=common difference and $a_1$= the first term Hence, here we have $a_n=1+(n-1)\cdot\left(-\dfrac{1}{3}\right)\\a_n=1+\left(-\dfrac{n}{3}\right)+\dfrac{1}{3}\\a_n=\dfrac{4}{3}-\dfrac{n}{3}\\a_n=\dfrac{4-n}{3}$ Therefore, $a_{51}=\dfrac{4-51}{3}\\a_{51}=-\dfrac{47}{3}$
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