121 ? 81 64 49 36 25

Options

A. 92
B. 114
C. 98
D. 100

Explanation

To solve the question of finding the missing number in the series: 121, ?, 81, 64, 49, 36, 25, we will follow these steps:

### Step 1: Identify the given series
The series provided is:
121, ?, 81, 64, 49, 36, 25.

### Step 2: Calculate the differences between consecutive numbers
To find the missing number, we will calculate the differences between the known consecutive numbers in the series:
- 81 - 64 = 17
- 64 - 49 = 15
- 49 - 36 = 13
- 36 - 25 = 11

So, the differences we have are:
17, 15, 13, 11.

### Step 3: Identify the pattern in the differences
Now, let's observe the differences:
- The difference between 17 and 15 is 2.
- The difference between 15 and 13 is 2.
- The difference between 13 and 11 is 2.

This shows that the differences are decreasing by 2 each time.

### Step 4: Determine the difference before 17
Following the identified pattern, the difference before 17 should be:
17 + 2 = 19.

### Step 5: Calculate the missing number
Now, we will subtract this difference (19) from the first number in the series (121) to find the missing number:
121 - 19 = 102.

### Step 6: Verify the series
To ensure our answer is correct, we can check the next number in the series:
- From 102, we subtract the next difference (17) to check if we arrive at 81:
102 - 17 = 85 (which is incorrect).

### Step 7: Correct the calculation
We need to find the correct missing number by using the identified differences correctly:
- The correct difference before 17 should be 21, not 19 (as we need to keep subtracting 2).
- Therefore, the missing number should be:
121 - 21 = 100.

### Step 8: Verify the series again
Now, let's verify:
- From 100, subtract 19 (the next difference):
100 - 19 = 81 (which is correct).

### Conclusion
The missing number in the series is **100**.