If&nbsp;f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals.&nbsp;

CAT 2018 Question Paper | CAT Verbal Ability Slot 1

Question :

If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals.

Started 1 month ago by Shashank in

Answer : The answer is '54'

Explanatory Answer

Given, f(x+2) = f(x) + f(x+1) f(11) = 91, f(15) = 617
We get 91 + f(12) = f(13)
Let f(12) be equal to some value ‘a’
So, 91 + a = f(13).
f(12) + f(13) = f(14)
a + 91 + a = f(14)
So, f(14) = 2a + 91 f(13) + f(14) = 617
So, 91 + a + 2a + 91 = 617
3a + 182 = 617
a = 145
Substituting the value of a and f(11), we get
f(10)+ 91 = 145
f(10) = 54