We want to find the geometric means in the given sequence. To do so, we first have to find the value of the common ratio r.
6, ?,?, 162
From the sequence, we know the value of the first term and that there are 4 total terms. We can substitute 6 for a_1 and 4 for n in the general formula for the n^(th) term of a geometric sequence.
a_n=a_1r^(n-1) ⇒ a_4= 6r^(4-1)
We also know that the value of the fourth term is 162. We can substitute this in the above formula and solve for r.
