Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Exercise Set - Page 1074: 60



Work Step by Step

We are given that the sequence $ a_n $ is a geometric sequence and the sequence $ b_n $ is an arithmetic sequence. Here, we have $ r=-2$ and $ d=-15$ The general formula to find the sum of first n term of a Geometric sequence is given as: $ S_{n}=\dfrac{a_1(1-r^n)}{(1-r)}$ Thus, $ S_{11}=\dfrac{(-5) \times (1-(-2)^{11})}{[1-(-2)]} \\=\dfrac{(-5) \times (1+2^{11})}{[1+2]}=-3415 $ The general formula to find the sum of the first n term of an Arithmetic sequence is given as: $ S'_{n}=\dfrac{n(b_1+b_n)}{2}$ and $ S'_{11}=\dfrac{11(b_1+b_1+(n-1)d)}{2} \\=\dfrac{11(10+10+(11-1) (-15))}{2}=-715$ Now, $ S_{110}+S'_{11}=-3415-715=-2700$
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