College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.2 - Arithmetic Sequences - 9.2 Assess Your Understanding - Page 654: 46

Answer

$301$

Work Step by Step

There is a constant difference, $3$, between terms. The terms are part of an arithmetic sequence. nth Term of an Arithmetic Sequence: $a_{n}=a_{1}+(n-1)d$ $ 41=2+3(n-1)\qquad$... solve for n $39=3(n-1)$ $13=(n-1)$ $n=14$ There are $14$ terms in the sum. The terms of the sum are the first $14$ terms of an arithmetic sequence, $a_{1}=2, d=3.$ Sum of the First $n$ Terms of an arithmetic sequence: $S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$ $S_{14}=\displaystyle \frac{14}{2}\left(2+41\right)=7\cdot 43=301$
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.