Question

If f (1) =4 and f(4)= f (n-1)-4 then find the value of f(4)

Answer 1

f(1) = 4 is given

f(n) = f(n-1)-4 is the recursive step or rule

f(2) = f(2-1)-4 ... replace n with 2

f(2) = f(1) - 4

f(2) = 4-4 ... replace f(1) with 4

f(2) = 0

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Repeat for n = 3

f(n) = f(n-1)-4

f(3) = f(3-1)-4

f(3) = f(2) - 4

f(3) = 0 - 4 .... replace f(2) with 0, which is from f(2) = 0 found earlier

f(3) = -4

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Repeat for n = 4

f(n) = f(n-1)-4

f(4) = f(4-1)-4

f(4) = f(3) - 4

f(4) = -4-4 ... plug in f(3) = -4

f(4) = -8

Answer is   -8