# Geometric progression formula

In this section of G.P. ask-math provides you geometric progression formula so that students can review it before the exam.
A sequence or a series of non-zero numbers is called a geometric progression if and only if the ratio of the term and the term preceding to it is always constant quantity. This constant is known as common ratio and it is denoted by 'r'.
If a1,a2,a3,... is a geometric progression then a1 + a2+ a3 + ... is a geometric series.

## Geometric progression formula

(i) The nth term of the G.P, with first term = a and common ratio = r is given by
$a_{n} = a r^{n - 1}$ where 'n' is the number of terms.

(ii) If geometric progression with 'm' terms and nth term from the end will be (m - n + 1)th term from the beginning is given by
$a_{n} = a r^{m - n}$

(iii) The sum of 'n' terms of a G.P. with first term = a and common ratio = r is
$S_{n} = a \frac{r^n - 1}{r -1}$ if r > 1

(iv) if r < 1
$S_{n} = a \frac{1 -r^n }{1 - r}$

(v) If r = 1 then $S_{n}$ = n
(vi) when last term = l
$S_{n} = a \frac{a - lr}{1 -r }$ if r <1

(vii) when last term = l
$S_{n} = a \frac{ lr - a}{r -1 }$ if r > 1

(viii) If a,b and c are in G.P and $b^{2}$ = ac then 'b' is a geometric mean of 'a' and 'c'.