If 2n-1 + 2n+1 = 320, then the value of n is = ?
A. 6
B. 8
C. 5
D. 7
Answer: Option D
Solution (By Examveda Team)
$$\eqalign{ & {\text{ }}{{\text{2}}^{n - 1}}{\text{ + }}{{\text{2}}^{n + 1}}{\text{ = 320}} \cr & \Rightarrow {\text{ }}{{\text{2}}^{n - 1}}\left( {1 + {2^2}} \right){\text{ = 320}} \cr & \Rightarrow {\text{ }}{{\text{2}}^{n - 1}} \times {\text{5 = 320}} \cr & \Rightarrow {\text{ }}{{\text{2}}^{n - 1}}{\text{ = }}\frac{{320}}{5}{\text{ = 64}} \cr & \Rightarrow {\left( 2 \right)^{n - 1}} = {\left( 2 \right)^6} \cr & \Rightarrow n - 1 = 6 \cr & \Rightarrow n = 7 \cr} $$This Question Belongs to Arithmetic Ability >> Surds And Indices
Sir 1+(2^2) kyu kiya
(1+2^2) how
2^n-1+2^n+1=320
2^n.2^-1+2^n.2^1=320
2^n(2^-1+2)=320
2^n(1/2+2)=320
2^n(5/2)=320
2^n=(320×5)/2
2^n=64
2^n=2^7
N=7
Answer is 7