**π Finding Specific Terms from the Sum of the First n Terms of a Geometric Sequence**

You can use the formula for the sum of a geometric series to help find a particular term of the series.

π Example 1: **Find the First Term of a Series**

Find *a*_{1} in a geometric series for which *S*_{8}=39,360 and *r*=3.

β Solution:

The first term of the series is 12.

π Example 2: **Determining the First Term of a Geometric Series**

The sum of the first 10 terms of a geometric series is -29,524.

The common ratio is -3. Determine the 1st term.

β Solution:

Suppose the geometric series has 1st term, *t*_{1}, and common ratio, *r*.

Use:

Substitute:

*n*=10,

*S*=-29,524,

_{n}*r*=-3

The 1st term is 2.

π Ex3. Find *a*_{1} if *S*_{12}=1,365 and *r*=2.

β Solution:

Substitute *S*_{12}=1, 365, *n*=12, and *r*=2 into the formula for the sum of a finite geometric series.

π Ex4. Find *a*_{1} if *S _{n}*=468,

*a*=375, and

_{n}*r*=5.

β Solution:

Substitute

*S*=468,

_{n}*a*=375, and

_{n}*r*=5 into the formula for the nth partial sum of an infinite geometric series.

Let’s read post πGet Last Term, Given the Sum of a Finite Geometric Seriesπ.