Question

Which term of the following sequence
$2,2\sqrt{2},4,...$ is $128$?

Answer 1

$r=\frac{2\sqrt{2}}{2}$

$r=\sqrt{2}$

$a_n=a_1{r}^{n-1}$

$128=2{\sqrt{2}}^{(n-1)}$

$\frac{128}{2}=2^{(n-1)/2}$

$2^6=2^{(n-1)/2}$

$6=\frac{n-1}{2}$

$n-1=12$

$n=13$

${13}^{th}$ term is $128$