Find the Third Term a_n=2(2)^n

$a_{n} = 2 {(2)}^{n}$

Substitute in the value of $n$ to find the $n$ th term.

$a_{3} = 2 {(2)}^{3}$

Multiply $2$ by ${(2)}^{3}$ by adding the exponents.

Multiply $2$ by ${(2)}^{3}$ .

Raise $2$ to the power of $1$ .

$a_{3} = 2 {(2)}^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a_{3} = 2^{1 + 3}$

Add $1$ and $3$ .

$a_{3} = 2^{4}$

Raise $2$ to the power of $4$ .

$a_{3} = 16$