Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.2 Arithmetic Sequences - 11.2 Assess Your Understanding - Page 835: 50



Work Step by Step

We can see that there are $80$ terms and these terms are part of an arithmetic sequence, so we have: $a_1=(3)-(2)(1)=1 \\ a_{90}=3-(2)(90)=-177$ There is a constant difference between the terms of: $d=a_{n+1}-a_n=3-2(n+1) -(3-2n)=3-2n-2-3+2n=-2$ The sum of the first $n$ terms of an arithmetic sequence is given by: $S_{n}= \dfrac{n}{2}\left(a_{1}+a_{n}\right) ..(1)$ Now, we plug in the above data into Equation-1 to obtain: $S_{90}= \dfrac{90}{2}[1+(-177)] \\=(45)(-176) \\= -7920$ Therefore, the sum of the arithmetic sequence is: $-7920$.
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