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 8.2 - Page 725: 56

Answer

Difference between the sum of first 15 terms of $b_{n}$ and the Sum of first 15 terms of $a_{n}$ = 570 -(- 405) = 570 + 405 = 975

Work Step by Step

From graph First term $a_{1}$ = 1 Second term $a_{2}$ = -3 Third term $a_{3}$ = -7 Common difference (d) = -7 + 3 = -3 - 1 = -4 $15^{th}$ term $a_{15}$ = 1 + (15 - 1)(-4) = 1 - 56 = -55 Sequence = 1, -3, -7, . . . . . -55 Sum of first 15 terms of $a_{n}$ = $\frac{15}{2}$(1 - 55) = $\frac{15}{2}$(- 54) = 15$\times$(-27) = -405 From graph First term $b_{1}$ = 3 Second term $b_{2}$ = 8 Third term $b_{3}$ = 13 Common difference (d) = 13 - 8 = 8 - 3 = 5 $15^{th}$ term $b_{15}$ = 3 + (15-1)5 = 3 + 70 = 73 Sequence = 3, 8, 13, . . . . . 73 Sum of first 15 terms of $b_{n}$ = $\frac{15}{2}$(3 + 73) = $\frac{15}{2}$(76) = 15$\times$38 = 570 Difference between the sum of first 15 terms of $b_{n}$ and the Sum of first 15 terms of $a_{n}$ = 570 -(- 405) = 570 + 405 = 975
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