College Algebra (10th Edition)

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

Chapter 9 - Section 9.3 - Geometric Sequences; Geometric Series - 9.3 Assess Your Understanding - Page 664: 41

Answer

$\displaystyle \frac{2^{n}-1}{4}$

Work Step by Step

$a_{1}=\displaystyle \frac{1}{4}$ $a_{2}=a_{1}\cdot 2$ $a_{3}=a_{1}\cdot 2^{2}$ $...$ The terms of the sum form a geometric sequence, $a_{1}=\displaystyle \frac{1}{4},\ r=2.$ THEOREM: Sum of the First $n$ Terms of a Geometric Sequence $S_{n}=a_{1}\displaystyle \cdot\frac{1-r^{n}}{1-r},\quad r\neq 0,1$ $=\displaystyle \frac{1}{4}\left(\frac{1-2^{n}}{1-2}\right)$ $=-\displaystyle \frac{1}{4}(1-2^{n})$ $=\displaystyle \frac{1}{4}(2^{n}-1)$
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.