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If 2n-1 + 2n+1 = 320, then the value of n is = ?
Answer & Solution
Correct Answer:
Option
D
$$\eqalign{
& {\text{ }}{{\text{2}}^{n - 1}}{\text{ + }}{{\text{2}}^{n + 1}}{\text{ = 320}} \cr
& \Rightarrow {\text{ }}{{\text{2}}^{n - 1}}\left( {1 + {2^2}} \right){\text{ = 320}} \cr
& \Rightarrow {\text{ }}{{\text{2}}^{n - 1}} \times {\text{5 = 320}} \cr
& \Rightarrow {\text{ }}{{\text{2}}^{n - 1}}{\text{ = }}\frac{{320}}{5}{\text{ = 64}} \cr
& \Rightarrow {\left( 2 \right)^{n - 1}} = {\left( 2 \right)^6} \cr
& \Rightarrow n - 1 = 6 \cr
& \Rightarrow n = 7 \cr} $$
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Login2^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