exponential sequence

A sequence of the form $x[n] = A\alpha^n$ -- growing, decaying, or (when $\alpha$ is complex) oscillating.

An exponential sequence $x[n] = A\alpha^n$ grows without bound when $|\alpha|>1$ , decays toward zero when $|\alpha|<1$ , and traces out a sinusoid when $\alpha = e^{j\omega}$ is complex with $|\alpha|=1$ -- the single family of sequences every LTI system's natural response is built from.