geometric sequence

A sequence is geometric if consecutive terms always have the same ratio r\neq 0, the common ratio: a_n = r\cdot a_{n-1}. Its explicit formula is a_n = a_1 r^{\,n-1}; when |r|>1 the terms grow without bound, when 0<|r|<1 they shrink toward zero, and when r<0 the signs alternate.