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

$$a _ { n } = ( 2 n ) ^ { 2 }$$

Solve for a_n

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

Solution Steps

Expand \left(2n\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

Solve for n (complex solution)

$$n=-\frac{\sqrt{a_{n}}}{2}$$

$$n=\frac{\sqrt{a_{n}}}{2}$$

Solve for n

$$n=-\frac{\sqrt{a_{n}}}{2}$$

$$n=\frac{\sqrt{a_{n}}}{2}\text{, }a_{n}\geq 0$$