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Question

If a function F is such that F(0)= 2, F (1) = 3, F (x + 2) = 2 F(x) – F (x -1) for x 0, then F(5) is equal to

A
-7
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B
-3
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C
17
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D
13
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Solution

The correct option is D 13
We have, F(x + 2) = 2 F (x) - F (x + 1) ….. (i)
x = 0 in (1) F (2) = 2F (0) - F (1) = 2 (2) - 3 = 1
x = 1 in (1) F(3) = 2F(1) - F (2) = 2 (3) - 1 = 5
x = 2 in (1) F (4) = 2 F (2) - F (3) = 2 (1) - 5 = -3
x = 3 in (1) F(5) = 2F (3) - F (4)
= 2(5) - (-3) = 13
The correct answer is (d).

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