Geometric Progression in Terms of Two Terms

Geometric Progression in Terms of Two Terms

## Formula

If the $$p$$th and $$q$$th terms of a GP are $a_p$ and $a_q$:

$$a_p=ar^{p-1}$$

$$a_q=ar^{q-1}$$

Therefore:

$$\frac{a_q}{a_p}=r^{q-p}$$

Hence:

$$r=\left(\frac{a_q}{a_p}\right)^{1/(q-p)}$$

## Usage

- Used when two terms of a GP are given and the common ratio is required.