## College Algebra (10th Edition)

Published by Pearson

# Chapter 9 - Section 9.3 - Geometric Sequences; Geometric Series - 9.3 Assess Your Understanding - Page 664: 28

#### Answer

$a_8=2187$

#### 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: $r = \dfrac{a_2}{a_1}=\dfrac{3}{1}=3$ Thus, the $n^{th}$ term of the sequence is given by the formula: $a_n = 1 \cdot 3^{n-1}$ The 8th term can be found by substituting $8$ for $n$: $a_8=1 \cdot 3^{9-1} \\a_8=1 \cdot 3^7 \\a_8 = 1 \cdot 2187 \\a_8=2187$

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