College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.1 - Sequences - 9.1 Assess Your Understanding: 74

Answer

$871$

Work Step by Step

RECALL: (1) $$\sum_{i=1}^{n}k = \dfrac{n(n+1)}{2}$$ (2) For any constant $c$, $$\sum_{i=1}^{n}c = nc$$ (3) For any constant $c$, $$\sum_{k=1}^{n}(k-c) = \sum_{k=1}^{n}k - \sum_{k=1}^{n}c$$ (4) For any constant $c$, $$\sum_{k=1}^{k}ck = c\sum_{k=1}^{n}k$$ Use rule (3) above to obtain: $$\sum_{k=1}^{26}(3k-7) = \sum_{k=1}^{26}(3k) - \sum_{k=1}^{26}7$$ Use rule (4) above to obtain: $$\sum_{k=1}^{26}(3k) - \sum_{k=1}^{26}7=3\sum_{k=1}^{26}k - \sum_{k=1}^{26}7$$ Use rule (1) and rule (2), respectively, to obtain: $$3\sum_{k=1}^{26}k - \sum_{k=1}^{26}7 \\=3\left(\dfrac{26(27)}{2}\right) - 26(7) \\=3(351) - 182 \\=1053 -182 \\=871$$
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