Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 11 - Further Topics in Algebra - Chapter 11 Test Prep - Review Exercises - Page 1082: 40

Answer

$$\sum\limits_{i = 1}^{20} {\left( {4i + 6} \right)} $$

Work Step by Step

$$\eqalign{ & 10 + 14 + 18 + \cdots 86 \cr & {\text{Calculating }}d{\text{ or }}r \cr & 14 - 10 = 4 \cr & 18 - 14 = 4 \cr & {\text{This is an arithmetic series with }}{a_1} = 10{\text{ and }}d = 4 \cr & {\text{The general term is }} \cr & {a_n} = {a_1} + \left( {n - 1} \right)d \cr & {a_n} = 10 + \left( {n - 1} \right)\left( 4 \right) \cr & {a_n} = 10 + 4n - 4 \cr & {a_n} = 4n + 6 \cr & {\text{The last term is }}86,{\text{ then}} \cr & 86 = 4n + 6 \cr & 80 = 4n \cr & n = 20 \cr & {\text{The sum of notation can be written as}} \cr & \sum\limits_{i = 1}^{20} {\left( {4i + 6} \right)} \cr} $$
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