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: 48



Work Step by Step

We have to determine the sum: $S=7+1-5-11-.....-299$ As $1-7=-5-1=-11-(-5)=...=-6$, the sequence is arithmetic. Determine its first term and the common difference: $a_1=7$ $d=-6$ Determine the number of terms: $a_n=a_1+(n-1)d$ $a_n-a_1=(n-1)d$ $n-1=\dfrac{a_n-a_1}{d}$ $n=\dfrac{a_n-a_1}{d}+1$ $n=\dfrac{-299-7}{-6}+1$ $n=52$ The given sum contains $52$ terms, so we have to determine the sum of the first $52$ terms. We use the formula: $S_n=\dfrac{n(a_1+a_n)}{2}$ $7+1-5-11-...-299=\dfrac{52(7-299)}{2}$ $=\dfrac{52\cdot (-292)}{2}$ $=-7592$
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