Q. The missing number in the series is:
4, 18, 48, ?, 180

Correct Answer: (B) 100

Explanation:

Step 1: Divide Each Term by Its Position
Let’s consider the position of each term in the series and divide the term by its position:

– 1st term: 4 / 1 = 4
– 2nd term: 18 / 2 = 9
– 3rd term: 48 / 3 = 16
– 4th term: ? / 4 = ?
– 5th term: 180 / 5 = 36

Step 2: Identify the Pattern
The resulting numbers after division are: 4, 9, 16, ?, 36. Observing these:

– 4 = 2²
– 9 = 3²
– 16 = 4²
– 36 = 6²

It appears that each of these numbers is a perfect square, and the pattern follows the sequence of squares of consecutive integers. Notably, the 4th term in this pattern should logically be 5² = 25.

Step 3: Calculate the Missing Term
Given that ? / 4 = 25, we can find the missing term:
? = 25 × 4 = 100

Answer: (B) 100