College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 7 - Section 7.1 - Sequences and Series - 7.1 Exercises - Page 636: 54

Answer

$-2$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To evaluate the given summation expression, $ \displaystyle\sum_{i=1}^4 (-3x_i-2) ,$ substitute $ i $ with the values from $ 1 $ to $ 4 .$ Then substitute the given values for each $x_i$'s $\bf{\text{Solution Details:}}$ Substituting $ i $ with the numbers from $ 1 $ to $ 5 ,$ the given expression is equivalent to \begin{array}{l}\require{cancel} (-3x_1-2)+(-3x_2-2)+(-3x_3-2)+(-3x_4-2) \\\\= -3x_1-2-3x_2-2-3x_3-2-3x_4-2 \\\\= (-3x_1-3x_2-3x_3-3x_4)+(-2-2-2-2) \\\\= (-3x_1-3x_2-3x_3-3x_4)+(-8) \\\\= (-3x_1-3x_2-3x_3-3x_4)-8 .\end{array} Factoring the common factor, $-3,$ in the expression $(-3x_1-3x_2-3x_3-3x_4-3x_5),$ results to \begin{array}{l}\require{cancel} -3(x_1+x_2+x_3+x_4)-8 .\end{array} Using the given values $x_1=-2,x_2=-1,x_3=0,$ and $x_4=1,$ the expression above evaluates to \begin{array}{l}\require{cancel} -3(-2+(-1)+0+1)-8 \\\\= -3(-2-1+0+1)-8 \\\\= -3(-2)-8 \\\\= 6-8 \\\\= -2 .\end{array}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.