GATE 2024 PH – Question 3
In the following series, identify the number that needs to be changed to form the Fibonacci series.
1, 1, 2, 3, 6, 8, 13, 21, ...
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Correct answer: (C) 6
Explanation
In a Fibonacci series each term is the sum of the two terms before it.
Given: 1, 1, 2, 3, 6, 8, 13, 21, ...
Check each term:
- $1+1=2$ ✓
- $1+2=3$ ✓
- $2+3=5$, but the series has **6** ✗
- Then $3+5=8$ ✓, $5+8=13$ ✓, $8+13=21$ ✓ (these work if the fifth term is 5).
The correct series is 1, 1, 2, 3, **5**, 8, 13, 21. The number that must be changed is **6** (option C).