Question

Find the 12th term of a G.P. whose 5th term is 64 and common ratio is 2.

Answer 1

We know that the formula for the $n$th term of an G.P is $T_n=a{r}^{n-1}$, where $a$ is the first term, $r$ is the common ratio.

It is given that the fifth term of G.P is $T_5=64$ and the common ratio is $r=2$, therefore,

$T_n=a{r}^{n-1}\Rightarrow T_5=a\times {\left(2\right)}^{5-1}\Rightarrow 64=a\times {\left(2\right)}^4\Rightarrow 64=16a\Rightarrow a=\frac{64}{16}=4$

Now we have the first term $a=4$ and the common ratio $r=2$, thus,

$T_{12}=4\times {\left(2\right)}^{12-1}=4\times {\left(2\right)}^{11}=4\times 2048=8192$

Hence, $T_{12}=8192$.