Question

If $F(n+1)=\frac{2F\left(n\right)+1}{2},n=1,2,.......$ and f(1) = 2 then f(101) equals

• A. 52
• B. 49
• C. 48
• D. 51

Answer 1

The correct option is A 52

$F(n+1)=\frac{2F\left(n\right)+1}{2}\Rightarrow F(n+1)-F\left(n\right)=\frac{1}{2}$

Put n = 1, 2, 3, ........, 100 and add, we get

$F\left(101\right)-F\left(1\right)=100\times \frac{1}{2}$

$\Rightarrow F\left(101\right)=52$