The nth term of a sequence is given by 22n−1 2 n − 1 . Find the sum of the first four terms.

The nth term of a sequence is given by 2${}^{2n-1}$. Find the sum of the first four terms.

Answer Details

$T_n=2^{2n-1}$
$T_1=2^{2\left(1\right)-1}$
= 2
$T_2=2^{2\left(2\right)-1}$
= 8
$T_3=2^{2\left(3\right)-1}$
= 32
$T_4=2^{2\left(4\right)-1}$
= 128
$T_1+T_2+T_3+T_4=2+8+32+128$
= 170