Xavier Aptitude Test 2016 Paper

Question : 62 of 103

Marks: +1, -0

f is a function for which f(1) = 1 and f(x) = 2x + f(x – 1) for each natural number x ≥ 2 . Find f(31).

869
929
951
991
None of the above

Solution:

(d) f(1) = 1
f(x) = 2x + f(x – 1)
f(2) = 2 × 2 + f (1)
f(2) = 2 × 2 + 1 ....(1)
f(3) = 2 × 3 + f(2)
f(3) = 2 × 3 + 2 × 2 + 1 ....(2)
Similarly f(31) = 2 × 31 + 2 × 30 + ....... +2 × 3 + 2 × 2 + 1
= 2 (31 + 30 + ......+ 3 + 2) + 1
= 2 ×

30/2

×33 + 1
= 991

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