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: 30

Answer

$a_{10}=512$

Work Step by Step

RECALL: (1) The $n^{th}$ term $a_n$ of a geometric sequence is given by the formula: $a_n=a_1 \cdot r^{n-1}$ where $a_1$ = first term $r$ = common ratio (2) The common ratio of a geometric sequence is equal to the quotient of any term and the term before it: $r = \dfrac{a_n}{a_{n-1}}$ The given geometric sequence has $a_1=-1$. Solve for the common ratio using the formula in (2) above to obtain: $r = \dfrac{a_2}{a_1}=\dfrac{2}{-1}=-2$ Thus, the $n^{th}$ term of the sequence is given by the formula: $a_n = -1 \cdot (-2)^{n-1}$ The 10th term can be found by substituting $10$ for $n$: $a_{10}=-1 \cdot (-2)^{10-1} \\a_{10}=-1 \cdot (-2)^9 \\a_{10} = -1 \cdot -512 \\a_{10}=512$
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