GATE 2022
August 11, 2023GATE 2023
August 11, 2023GATE 2023
| Question 3 |
A series of natural numbers F1, F2, F3, F4, F5, F6, F7, … obeys Fn+1 = Fn + Fn-1 for all integers n >= 2 . If F6 = 37, and F7 = 60, then what is F1 ?
| 4 | |
| 5 | |
| 8 | |
| 9 |
Question 3 Explanation:
Given series is Fibonacci series
F(n+1)=F(n)+F(n-1)
Given values are F(6) is 37 and F(7) is 60
F(7)=F(6)+F(5) → 60=37+F(5) → F(5) =60-37=23
F(6)=F(5)+F(4) → 37=23+F(4) → F(4) =37-23=14
F(5)=F(4)+F(3) → 23=14+F(3) → F(3) =23-14=9
F(4)=F(3)+F(2) → 14=9+F(2) → F(2) =14-9=5
F(3)=F(2)+F(1) → 9=5+F(1) → F(1) =9-5=4
F(n+1)=F(n)+F(n-1)
Given values are F(6) is 37 and F(7) is 60
F(7)=F(6)+F(5) → 60=37+F(5) → F(5) =60-37=23
F(6)=F(5)+F(4) → 37=23+F(4) → F(4) =37-23=14
F(5)=F(4)+F(3) → 23=14+F(3) → F(3) =23-14=9
F(4)=F(3)+F(2) → 14=9+F(2) → F(2) =14-9=5
F(3)=F(2)+F(1) → 9=5+F(1) → F(1) =9-5=4
Correct Answer: A
Question 3 Explanation:
Given series is Fibonacci series
F(n+1)=F(n)+F(n-1)
Given values are F(6) is 37 and F(7) is 60
F(7)=F(6)+F(5) → 60=37+F(5) → F(5) =60-37=23
F(6)=F(5)+F(4) → 37=23+F(4) → F(4) =37-23=14
F(5)=F(4)+F(3) → 23=14+F(3) → F(3) =23-14=9
F(4)=F(3)+F(2) → 14=9+F(2) → F(2) =14-9=5
F(3)=F(2)+F(1) → 9=5+F(1) → F(1) =9-5=4
F(n+1)=F(n)+F(n-1)
Given values are F(6) is 37 and F(7) is 60
F(7)=F(6)+F(5) → 60=37+F(5) → F(5) =60-37=23
F(6)=F(5)+F(4) → 37=23+F(4) → F(4) =37-23=14
F(5)=F(4)+F(3) → 23=14+F(3) → F(3) =23-14=9
F(4)=F(3)+F(2) → 14=9+F(2) → F(2) =14-9=5
F(3)=F(2)+F(1) → 9=5+F(1) → F(1) =9-5=4
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