Question

What is the formula of GP?

Answer 1

A geometric progression is a sequence in which each consecutive element is obtained by multiplying the preceding element by a constant. The constant value is called a common ratio.

The general form of an GP: $a,ar,a{r}^2,a{r}^3,.....$ , where $a$ is the first term and $r$ is a common ratio.

Formulas:

• For $n^{th}$ term in GP: $a_n=a{r}^{n-1}$
• For common ratio: $r=\frac{a_n}{a_{n-1}}$
• Sum of $n$ terms:

$S=a\left[\frac{\left(r^n-1\right)}{\left(r-1\right)}\right],r>1$

$S=a\left[\frac{\left(1-r^n\right)}{\left(1-r\right)}\right],r<1$

• Sum of infinite terms in GP: $S=\left[\frac{a}{\left(1-r\right)}\right],-1<r<1$