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: 55

Answer

Difference between the sum of first 14 terms of $b_{n}$ and the Sum of first 14 terms of $a_{n}$ = 497 - (-350) = 497 +350 = 847

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 $14^{th}$ term $a_{14}$ = 1 + (14 - 1)(-4) = 1 - 52 = -51 Sequence = 1, -3, -7, . . . . . -51 Sum of first 14 terms of $a_{n}$ = $\frac{14}{2}$(1 - 51) = 7$\times$(-50) = -350 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 $14^{th}$ term $b_{14}$ = 3 + (14-1)5 = 3 + 65 = 68 Sequence = 3, 8, 13, . . . . . 68 Sum of first 14 terms of $b_{n}$ = $\frac{14}{2}$(3 + 68) = 7$\times$71 = 497 Difference between the sum of first 14 terms of $b_{n}$ and the Sum of first 14 terms of $a_{n}$ = 497 - (-350) = 497 +350 = 847
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