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: 42



Work Step by Step

We have to determine the sum: $S=-1+3+7+.....+(4n-5)$ As $3-(-1)=7-3=...=4$, the sequence is arithmetic. Determine its first term and the common difference: $a_1=-1$ $d=4$ The given sum contains $n$ terms; therefore we have to determine the sum of the first $n$ terms. We use the formula: $S_n=\dfrac{n(a_1+a_n)}{2}$ $-1+3+7+...+(4n-5)=\dfrac{n(-1+4n-5)}{2}$ $=\dfrac{n(4n-6)}{2}$ $=n(2n-3)$ $=2n^2-3n$
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