Question

Find the ${11}^{\mathrm{th}}$ term of the GP :$3,6,12,24,\dots .$

Answer 1

Find the ${11}^{th}$term of GP:

Here, the sequence is $3,6,12,24,\dots .$

First term $a=3$
Common difference $r=\frac{6}{3}=2$

Formula:

The general term of GP is $\begin{array}{rcl}{a}_n& =& a{r}^{n-1}\end{array}$ .

$\begin{array}{rcl}& \Rightarrow & a_{11}=3\times 2^{11-1}\\ & =& 3\times 2^{10}\\ & =& 3072\end{array}$

Hence, the $n^{th}$term of given GP is $3072$.