Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.7 Arithmetic and Geometric Sequences - Exercise Set 5.7: 27

Answer

$a_{200}=955$

Work Step by Step

The $n^{th}$ term of an arithmetic sequence can be found using the formula: $a_n = a_1 + (n-1)d$ where d = common difference $a_1$ = first term $\\a_n= n^{th} \text{ term}$ The given arithmetic sequence has: $a_1 = -40 \\d=5$ Use the formula above to find the 200th term: $a_n=a_1+(n-1)(d) \\a_{200}=-40 + (200-1)5 \\a_{200}=-40+199(5) \\a_{200}=-40+995 \\a_{200}=955$
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