If 2n-1 + 2n+1 = 320, then the value of n is = ?

Answer: Option D

$$\begin{array}{rl}& {\text{2}}^{n-1}\text{ + }{\text{2}}^{n+1}\text{ = 320}\\ & \Rightarrow {\text{2}}^{n-1}\left(1+2^2\right)\text{ = 320}\\ & \Rightarrow {\text{2}}^{n-1}\times \text{5 = 320}\\ & \Rightarrow {\text{2}}^{n-1}\text{ = }\frac{320}{5}\text{ = 64}\\ & \Rightarrow {\left(2\right)}^{n-1}={\left(2\right)}^6\\ & \Rightarrow n-1=6\\ & \Rightarrow n=7\end{array}$$