Question

Find the
th term of a geometric sequence where the
nd term is
and the common ratio is
.

Answer 1

It looks like some numbers are missing from your question. In general, if a geometric sequence has common ratio r and its nth term is a_n, then the kth term a_k (i.e., the "th term" you want) is

a_k = a_n · r^(k−n).

Derivation: a_n = a_1 r^(n−1) and a_k = a_1 r^(k−1), so a_k = a_n · r^(k−n).

Also useful:
- the first term: a_1 = a_n / r^(n−1)
- if you instead know a_1 and r, then a_k = a_1 · r^(k−1)

If you give the specific n, a_n, r and which term k you want, I can compute the numeric answer.