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If a function F is such that F(0)=2, F(1...

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

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The correct Answer is:
13
Given , F(0) = 2 , F(1) = 3
Since , `F(n+2)=2F(n)-F(n+1)`
At `n = 0 , F (0+2)= 2F (0)-F(1)" "implies " "F(2)=2(2)-3=1`
At `n = 1 , F (1+2)= 2F (1)-F(2)" "implies " "F(3)=2(3)-1=5`
At `n=2 , F (2+2)=2F(2)-F(3)impliesF(4)=2 (1)-5=-3`
At `n=3 , F (3+2)=2F(3)-F(4)=2(5)-(-3)`
`implies F(5) = 13`
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