CAT 2018 Question Paper Shift 1 Solved Paper

Question : 88 of 100

Marks: +1, -0

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

Solution:

f(x+2)=f(x)+f(x+1)

{f}(11)=91

Let

f(12)=a

f(13)=91+a

{f}(14)=91+2 {a}

f(15)=182+3 a

This is also equal to

617

182+3 a=617 ⇒ a=145

f(10)=f(12)-f(11)=145-91=54

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