The common ratio in a geometric sequence is 3/2, and the fifth term is 1. How do you find the first three terms?

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Answer 1 · 2016-05-22T06:28:39

$16/81$ , $8/27$ , $4/9$

The formula for finding the $n^"th"$ ( $U_n$ ) term in a geometric sequence is

$U_n=U_1xxr^"n-1"$

where $r$ is the common ratio.

$U_1 = ?$
$U_5 = 1$
$r = 3/2$

$U_5=U_1xx(3/2)^"5-1"$

$1=U_1xx(3/2)^"4"$

Rearrange

$1/(3/2)^"4"=U_1$

$U_1=1/(81/16)=16/81$

$U_2=16/81xx3/2=8/27$

$U_3=8/27xx3/2=4/9$