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: 16


$a_n=-2+4(n-1)$ and $a_{51} =198$

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: $a_1=-2 \\ d=4$ Next, we will substitute the above data into the formula (1) to obtain: $a_n=-2+(4)(n-1) \implies a_n=-2+4(n-1)$ In order to compute the $51st$ term, we need to plug in $51$ for $n$ into the above form to obtain: $a_{51} = -2+4(51-1) =-2+200$ So, $a_{51} =198$
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