How do you find the 7th term of the geometric sequence with the given terms a4 = 54, a5 = 162?

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Answer 1 · 2016-01-20T03:23:37

$a_7 = 1458$

Since this is a geometric sequence we know the following

$a_n= a_1r^(n-1)$ noticed we started at 1 that why we subtract 1 from n

the ratio $r = (a_n)/(a_(n-1))$

We are given

$a_4 =54 " " " a_5= 162$

We first, need to find $r$

$r= (a_5)/(a_4) = 162/54 = 3$

Then we can use the formula $a_n = a_1r^(n-1)$

(but instead of finding $a_1$ , we will use $a_4$ we need to subtract 4 from the nth term

$a_7= a_4r^(7-4)$

$a_7 = (54)(3)^(3)$

$" a_7 = 1458$