Q. What would be the next in the following series?144, 100, 64, 36, ?

Q. What would be the next in the following series?
144, 100, 64, 36, ?

(ADRE 2024)

(A) 25

(B) 49

(C) 81

(D) 16

Answer:- (D) 16

Solution:- 

To find the next number in the series 144, 100, 64, 36, let’s analyze the pattern:

• 144 = 12²
• 100 = 10²
• 64 = 8²
• 36 = 6²

The following patterns are observed:-

• The given series is a sequence of perfect squares.
• The series comprises perfect squares of even numbers:$12, 10, 8, 6$
• The sequence of even numbers is decreasing by 2 each time.

Next number:-

• The next even number in the above series after 6 is 4.
• So, following the pattern, the next number should be the square of 4.
• 4² = 16

Therefore, the next number in the series is 16.

So, the answer is Option (D) 16.