Monotonicity of a GP

Monotonicity of a GP

## Formula

For:

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

the behaviour depends on both $$a$$ and $$r$$.

For positive $$a$$:

$$r>1\Rightarrow a_{n+1}>a_n$$

$$0<r<1\Rightarrow a_{n+1}<a_n$$

$$r=1\Rightarrow a_{n+1}=a_n$$

For:

$$r<0$$

the signs alternate.

## Usage

- Used to determine the increasing or decreasing behaviour of a GP.