what is the formula of geometric sequence

A geometric sequence is a sequence of numbers in which the ratio of every two consecutive numbers is always a constant. The general form of the geometric sequence formula is: $$a_n=a_1r^{(n-1)}$$ where $r$ is the common ratio, $a_1$ is the first term, and $n$ is the placement of the term in the sequence. The formula for the sum of the first $n$ terms of a geometric sequence is: $$S_n = a\frac{1-r^n}{1-r}$$ where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms being summed.