CAT 2018 Slot 1 — QA Question 26
Basics (Functions)Easy
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
Answer & solution
Answer: 54
Solution
f(x + 2) = f(x) + f(x + 1)
Subtituting x = 13
f(15) = f(14) + f(13)
= [f(13) + f(12)] + f(13)
= 2 × f(13) + f(12)
= 2[f(12) + f(11)] + f(12)
= 3 × f(12) + 2 × f(11)
= 3[f(11) + f(10)] + 2 × f(11)
= 5 × f(11) + 2 × f(10)
∴ 617 = 5 × 91 + 3 × f(10)
Solving this we get, f(10) = 54
Hence, 54.