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: 41



Work Step by Step

We have to determine the sum: $S=7+12+17+.....+(2+5n)$ As $12-7=17-12=...=5$, the sequence is arithmetic. Determine its first term and the common difference: $a_1=7$ $d=5$ The given sum contains $n$ terms; therefore we have to determine the sum of the first $n$ terms. We use the formula: $S_n=\dfrac{n(a_1+a_n)}{2}$ $7+12+17+...+(2+5n)=\dfrac{n(7+2+5n)}{2}=\dfrac{n(5n+9)}{2}$
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