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F(n)

by shashank.ism » Mon Feb 08, 2010 7:05 am
A function f(n) is defined for all positive real values of 'n' such that f(n + 2) = f(n + 1) + f(n).
If f(1) = f(2) = 1, then find the highest common factor of f (12) and f (30)

a) f(11)
b) f(4)
c) f(6)
d) f(3)
e) f(5)
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by harsh.champ » Mon Feb 08, 2010 7:08 am
shashank.ism wrote:A function f(n) is defined for all positive real values of 'n' such that f(n + 2) = f(n + 1) + f(n).
If f(1) = f(2) = 1, then find the highest common factor of f (12) and f (30)

a) f(11)
b) f(4)
c) f(6)
d) f(3)
e) f(5)
Putting n = 1
f(3) = f(2) + f(1)= 2
n=2
f(4) = f(3) + f(2) =3
n=3
f(5) = f(4) + f(3) = 5
n=4
f(6) = f(5) + f(4) = 8
n=5
f(7) = f(6) + f(5) = 13

Hence we get a series, 1+1+2+3+5+8+13+.......
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