Find the specified term of the following geometric sequence.
1. 2, 6, 18, … the 8
th term
2. 3, 6, 12, … the 9
th term
3. 81, 54, 36, … 5th term
4. 64, -32, 16, … 6th term
5.64, -96, 144, … 7th term
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Elementary and Intermediate Algebra (5th) Edition 1133710808 9781133710806
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Elementary and Intermediate Algebra
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Chapter
Chapter List
CH14.3
Problem
Problem List
21SS
Find the specified term of the geometric sequence with the following properties. See Example.
Example
EXAMPLE The first three terms of a geometric sequence are 16, 4, and 1. Find the 7th term.
Strategy We can use the first three terms to find the common ratio. Then we will know the first term and the common ratio.
Why Once we know the first term, a1, and the common ratio, r, we can use the formula an = a1rn−1 to find the seventh term by letting n = 7.
Solution The common ratio r is the ratio between any two successive terms. Since a1 = 16 and a2 = 4, we can find r as follows:
To find the seventh term, we substitute 16 for a1, for r, and 7 for n in the formula for the nth term and simplify:
The first three terms are , ,; find the 6th term
Answer:
so, this is the specified term of the following geometric sequence.
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