Given a geometric sequence with the first term *a*_{1} and the common ratio *r*, the ** n^{th} (or general) term** is given by

**Example 1:**

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

**Example 2:**

Find the 7^{th} term for the geometric sequence in which

a_{2} = 24 and *a*_{5} = 3.

Substitute 24 for *a*_{2} and 3 for *a*_{5} in the formula
*a _{n}* =

Substitute this expression for* a*_{1} in the second equation and solve for *r*.

Substitute for *r* in the first equation and solve for* a*_{1}.

Now use the formula to find *a*_{7}.