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GATE CS 2023 · General Aptitude

Question 3

MCQ1 markWrong answer: −1/3Easy (estimate)

Question

A series of natural numbers F1,F2,F3,F4,F5,F6,F7,…F_1, F_2, F_3, F_4, F_5, F_6, F_7, \dots obeys Fn+1=Fn+Fn−1F_{n+1} = F_n + F_{n-1} for all integers n≥2n \ge 2.

If F6=37F_6 = 37, and F7=60F_7 = 60, then what is F1F_1?

Choose one option
Official answer and solution
Official answer
A
From
Official GATE 2023 answer key

Solution

Work backwards from the given values using the recurrence relation Fn−1=Fn+1−FnF_{n-1} = F_{n+1} - F_n.

We are given Fn+1=Fn+Fn−1F_{n+1} = F_n + F_{n-1}, which rearranges to Fn−1=Fn+1−FnF_{n-1} = F_{n+1} - F_n.

Given F7=60F_7 = 60 and F6=37F_6 = 37:

  1. F5=F7−F6=60−37=23F_5 = F_7 - F_6 = 60 - 37 = 23
  2. F4=F6−F5=37−23=14F_4 = F_6 - F_5 = 37 - 23 = 14
  3. F3=F5−F4=23−14=9F_3 = F_5 - F_4 = 23 - 14 = 9
  4. F2=F4−F3=14−9=5F_2 = F_4 - F_3 = 14 - 9 = 5
  5. F1=F3−F2=9−5=4F_1 = F_3 - F_2 = 9 - 5 = 4
Final answer

Option (A)

Common trap

Stopping at F2=5F_2 = 5 instead of computing down to F1=4F_1 = 4.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2023 Computer Science and Information Technology (CS)
Question
3 of 65
Section
General Aptitude

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