What comes next in the following series?
A1, B1, C4, D9, E25, F64, ?
Show answer & explanation
Correct answer: C
Explanation
Given Series: A1, B1, C4, D9, E25, F64, ?
pattern in letters:
The letters are in alphabetical order: A, B, C, D, E, F, ... So the next letter will be G.
Pattern in numbers
The numbers are: 1, 1, 4, 9, 25, 64
These correspond to:
1=12
1=12(repeated)
4=22
9=32
25=52
64=82
The sequence of square roots is: 1, 1, 2, 3, 5, 8 — which is the Fibonacci sequence where each term is the sum of the previous two.
The next Fibonacci number after 8 is:
5+8=13
So, the next term's number is:
132 =169
Therefore, the next term is G169
Hence, the correct answer is option (3).