Find the Nth term in the geometric sequence where the first term is 3 and the fourth term is 6√2

Emmy Swanson 2022-10-22 Answered
Find the Nth term in the geometric sequence where the first term is 3 and the fourth term is 6 2
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Answers (1)

Szulikto
Answered 2022-10-23 Author has 22 answers
The general term of a geometric sequence can be written:
a n = a r n - 1
where a is the initial term and r the common ratio.
In our case we are given a 1 = 3 and a 4 = 6 2
So we find:
r 3 = a r 3 a r 0 = a 4 a 1 = 6 2 3 = 2 2 = ( 2 ) 3
So (assuming the geometric sequence is Real):
r = 2 3 3 = 2
and
a n = 3 ( 2 ) n - 1 = 3 2 n - 1 2
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