College Algebra (10th Edition)

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

Chapter 9 - Test - Page 680: 10

Answer

See below.

Work Step by Step

In order for a sequence to be geometric, the quotient of all consecutive terms must be constant. Hence here: $\frac{10}{25}=\frac{4}{10}=0.4=r$, thus it is a geometric sequence. Hence it is a geometric sequence. The sum of a geometric sequence until $n$ can be obtained by the formula $S_n=a_1(\frac{1-r^n}{1-r})$ where $a_1$ is the first term and $r$ is the common ratio. Hence here the sum is: $S_n=25(\frac{1-0.4^n}{1-0.4})$.
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