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Question

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


A
52
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B
49
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C
48
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D
51
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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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