Increasing Sequence

For a Sequence $\{a_n\}$, if $a_{n+1}-a_n > 0$ for $n \geq x$, then $a_n$ is increasing for $n \geq x$. Conversely, if $a_{n+1}-a_n < 0$ for $n \geq x$, then $a_m$ is Decreasing for $n \geq x$.

If $a_n>0$ and ${a_{n+1}/a_n} >1$ for all $n \geq x$, then $a_n$ is increasing for $n \geq x$. Conversely, if $a_n>0$ and ${a_{n+1}/ a_n} < 1$ for all $n \geq x$, then $a_n$ is decreasing for $n \geq x$.

See also Decreasing Sequence, Sequence