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: 40

Answer

$a_6=-648$

Work Step by Step

To find the sixth 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, $r=\dfrac{a_2}{a} \\r=\dfrac{-\frac{1}{2}}{\frac{1}{12}} \\r=-\dfrac{1}{2} \cdot \dfrac{12}{1} \\r=-\dfrac{12}{2} \\r=-6$ The sixth term can be found by multiplying the common ratio $r$ to the second term four times: $a_6 = a_2 \cdot r \cdot r \cdot r \cdot r \\a_6=a_2 \cdot r^4 \\a_6 = -\dfrac{1}{2} \cdot (-6)^4 \\a_6 = -\dfrac{1}{2} \cdot 1296 \\a_6=-648$
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