Question

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

A
52
B
49
C
48
D
51

Solution

## The correct option is A 52$$F(n + 1) = \frac {2F(n) + 1} {2} \Rightarrow F(n + 1) - F(n) = \frac{1} {2}$$Put n = 1, 2, 3, ........, 100 and add, we get$$F(101) - F(1) = 100 \times \frac{1} {2}$$$$\Rightarrow F(101) = 52$$Mathematics

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