Sum of a GP Using First and Last Terms

Sum of a GP Using First and Last Terms

## Formula

For a GP with first term $$a$$, last term $$l$$, common ratio $$r$$ and $$n$$ terms:

$$S_n=a\frac{r^n-1}{r-1}$$

Since:

$$l=ar^{n-1}$$

we can also write:

$$S_n=\frac{lr-a}{r-1}$$

for:

$$r\ne1$$

## Usage

- Used when the first and last terms and common ratio are known.