Finding the nth Term of a Geometric Sequence

Given a geometric sequence with the first term a1 and the common ratio r, the nth (or general) term is given by
an = a1 · rn1.

Example 1:

Find the 6th term in the geometric sequence 3, 12, 48,···.

Example 2:

Find the 7th term for the geometric sequence in which
a
2 = 24 and a5 = 3.
Substitute 24 for a2 and 3 for a5 in the formula
an = a1 · rn1.

Substitute this expression for a1 in the second equation and solve for r.



Substitute for r in the first equation and solve for a1.



Now use the formula to find a7.