Correct Answer:
Option B —
72
Step-by-Step Logic
1. Find the differences between the known terms:
36 - 11 = 25
266 - 185 = 81
185 - 121 = 64
2. Analyze the sequence of differences:
The differences we found are:
25 (which is 5^2)
64 (which is 8^2)
81 (which is 9^2)
3. Identify the missing squares:
The pattern follows the squares of consecutive integers starting from 5
Difference 1: 5^2 = 25
Difference 2: 6^2 = {36} (Missing)
Difference 3: 7^2 = {49} (Missing)
Difference 4: 8^2 = 64
Difference 5: 9^2 = 81
4. Calculate the missing term:
Take the second term and add the next square (6^2 = 36): 36 + 36 = {72}
5. Verify the pattern: Add the next square (7^2 = 49 ) to our result to see if it matches the next term in the series: 72 + 49 = 121
The value 121 matches the series provided, confirming that 72 is the correct missing number.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
