Question

A G.P. is a sequence whose first term is non-zero and each of whose succeeding term is $r$ times the preceding term, where $r$ is some fixed non-zero number, known as the common ratio of the G.P. If $a$ if the first term of a G.P. and $r$ its common ratio, then its $n^{th}$ term $t_n$ is given by $t_n=a{r}^{n-1}$.

Answer 1

Considering,

a as first term of G.P.

r as common ratio of G.P.

then the G.P. series is given by,

$a,ar,a{r}^2,...............,a{r}^n$

nth term is given by,

$t_n=a{r}^{n-1}$

sum of the G.P. series is given by,

$S_n=\frac{a(r^n-1)}{r-1}$