Find the 7th term of the geometric sequence with the given terms a_4 = 54, a_5 = 162

Leonel Schwartz

Leonel Schwartz

Answered question

2022-10-03

Find the 7th term of the geometric sequence with the given terms a 4 = 54 , a 5 = 162

Answer & Explanation

Derick Ortiz

Derick Ortiz

Beginner2022-10-04Added 11 answers

Since this is a geometric sequence we know the following
a n = a 1 r 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 1 r 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 4 r 7 - 4
a 7 = ( 54 ) ( 3 ) 3
a 7 = 1458

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