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

$a_n=128$

$a.r^{n-1}=128$

$2{\left(\sqrt{2}\right)}^{n-1}=2^7$

${2.2}^{\frac{n-1}{2}}=2^7$

$2^{1+\frac{n-1}{2}}=2^7$

$2^{\frac{2+n-1}{2}}=2^7$

$2^{\frac{n+1}{2}}=2^7$

$\frac{n+1}{2}=7$

$n+1=14$

$n=13$

${13}^{\text{th}}\text{term}$