Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Concept and Vocabulary Check - Page 1073: 6


The first four terms of the series $\sum\limits_{i=1}^{6}{{{2}^{i}}}$ are $2;{{2}^{2}};{{2}^{3}};{{2}^{4}}$. The common ratio is 2.

Work Step by Step

In order to find the terms of the series $\sum\limits_{i=1}^{6}{{{2}^{i}}}$, we have to replace i in the expression ${{2}^{i}}$ with all the consecutive integers from 1 to 6. Hence, the first term is obtained as $ i~=\text{ }1,~{{2}^{1}}$ Then, the second term is obtained as i = 1, ${{2}^{2}}$ Similarly the third term is obtained as i = 1, ${{2}^{3}}$ And the fourth term is obtained as i = 1, ${{2}^{4}}$
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