Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set: 38

Answer

$S_{50}=2500$

Work Step by Step

The first n term of an arithmetic sequence can be calculated as: $S_n=\frac{n}{2}(a_1+a_n)$ We have to find the sum of the odd numbers from 1 to 99. $a_1=1$ $a_{n}=99$ There are 50 odd numbers from 1 to 99, inclusive. Therefore we can substitute in the formula of the sum, and we get: $S_{50}=\frac{50}{2}(1+99))=25\times100=2500$
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