Question

Find the Missing Number: 
2, 12, 36, 80, 150, ?

• A. 195
• B. 210
• C. 252
• D. 258

Hint:

When solving number series problems, check the differences between terms and look for a pattern in the differences, such as constant or increasing differences.

Answer 1

The Correct Option is C

Step 1: Let’s analyze the given sequence: 2, 12, 36, 80, 150, ?. 
Step 2: Calculate the differences between consecutive terms: - \( 12 - 2 = 10 \) - \( 36 - 12 = 24 \) - \( 80 - 36 = 44 \) - \( 150 - 80 = 70 \) The differences between consecutive terms are 10, 24, 44, and 70. 
Step 3: Now, let's look at the second differences: - \( 24 - 10 = 14 \) - \( 44 - 24 = 20 \) - \( 70 - 44 = 26 \) The second differences are 14, 20, and 26, which increase by 6. 
Step 4: If we continue this pattern, the next second difference should be \( 26 + 6 = 32 \). 
Step 5: Now, let's find the next first difference:- \( 70 + 32 = 102 \) 
Step 6: Finally, add this difference to the last term in the sequence:- \( 150 + 102 = 252 \) Thus, the missing number is 252. 
Thus, the correct answer is option (C) 252.