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A function F satisfies F(0) = 2, F(1) = 3, and the recurrence relation F(x + 2) = 2F(x) - F(x + 1) for all integers x >= 0. Find F(5).

1. -7
2. -3
3. 17
4. 13

Correct answer: 13

Solution

Using the recurrence iteratively: F(2) = 2F(0) - F(1) = 1. F(3) = 2F(1) - F(2) = 5. F(4) = 2F(2) - F(3) = -3. F(5) = 2F(3) - F(4) = 10 - (-3) = 13.

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