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If f(1)= 1, f(2)=3, and f(n) =2f (n-1) -f (n-2) then find the value of f (5).

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Answer:

f[5] = 9

Explanation:

We can work this one term at a time.

f[3] = 2f[2] -f[1] = 2(3) -(1) = 5

f[4] = 2f[3] -f[2] = 2(5) -3 = 7

f[5] = 2f[4] -f[3] = 2(7) -5 = 9

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Additional comment

The terms known to this point seem to indicate f[n] = 2n -1 is a workable simplification. Or, recursively, f[n] = f[n-1] +2.

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