College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.3 - Geometric Sequences - 8.3 Exercises: 39

Answer

$a_4 = \dfrac{24}{25}$

Work Step by Step

To find the fourth term, the value of the common ratio $r$ is needed. The value $r$ can be found by dividing the second term by the first term of the sequence. Thus, $r=\dfrac{a_2}{a} \\r=\dfrac{6}{15} \\r=\dfrac{2}{5}$ The fourth term can be found by multiplying the common ratio $r$ to the second term twice: $a_4 = a_2 \cdot r \cdot r \\a_4 = 6 \cdot \dfrac{2}{5} \cdot \dfrac{2}{5} \\a_4 = \dfrac{24}{25}$
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