Geometric Sequence

A geometric sequence is a Sequence $\{a_k\}$, $k=1$, 2, ..., such that each term is given by a multiple $r$ of the previous one. Another equivalent definition is that a sequence is geometric Iff it has a zero Bias. If the multiplier is $r$, then the $k$th term is given by

$$a_k=r a_{k-1} = r^2 a_{k-2} = a_0r^k.$$

Without loss of generality, take $a_0=1$, giving

$$a_k=r^k.$$