College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 8 - Sequences, Induction, and Probability - Exercise Set 8.1 - Page 715: 58


$\displaystyle \sum_{k=1}^{15}ar^{k-1}$ (sample answer)

Work Step by Step

Remembering that $r^{0}=1$, we can write the first term as $ar^{0}$, (for k=1, the exponent is k-1) Observing the terms, counting them as k=2 (second), k=3 (third), etc, $ar^{1}$, (for k=2, the exponent is k-1) $ar^{2}$, (for k=3, the exponent is k-1) ... The pattern suggests that the general, k-th term is${}_{\text{ }} ar^{k-1}$ So, we have terms from 1 to 15, (the exponent in the last term is 14 = 15-1), and we write the sum as $\displaystyle \sum_{k=1}^{15}ar^{k-1}$ (sample answer)
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