Pattern Analysis:
To find the missing term in the given number series, let's analyze the pattern in the given terms:

- The given series is a sequence of perfect squares.
- The first term, 121, is the square of 11.
- The second term, 225, is the square of 15.
- The third term, 361, is the square of 19.

Identifying the Pattern:
From the above analysis, we can observe that the difference between consecutive terms in the series is increasing by 4 each time. Let's verify this pattern:

- The difference between the second and first terms is 225 - 121 = 104.
- The difference between the third and second terms is 361 - 225 = 136.

Both differences are multiples of 4, indicating a consistent pattern.

Using the Pattern to Find the Missing Term:
To find the missing term, we need to continue the pattern and determine the next square in the sequence. Let's apply the pattern:

- The difference between the third and second terms is 136.
- Adding 4 to this difference, we get 136 + 4 = 140.
- Therefore, the difference between the missing term and the third term should be 140.

Calculating the Missing Term:
To find the missing term, we add the calculated difference to the third term:

361 + 140 = 501.

However, this result is not a perfect square and does not match any of the given options.

Alternative Approach:
Let's try a different approach to see if there is another pattern in the given series:

- The difference between the second and first terms is 104.
- The difference between the third and second terms is 136.
- Calculating the difference between these two differences, we get 136 - 104 = 32.

Applying the Alternative Pattern:
To find the missing term, we can try adding this difference of 32 to the third term:

361 + 32 = 393.

However, this result is not a perfect square and does not match any of the given options.

Conclusion:
Based on the analysis and calculations, it seems that neither of the patterns identified can be consistently applied to find the missing term. Therefore, it is possible that the given series does not follow a clear pattern, or there may be an error in the question itself. As none of the given options match the alternative calculations, it is difficult to determine the correct answer.

121=11×11 225=15×15 361=19×19 529=23×23 the sequence has increases by 4 11to 15 increase by 4 15 to 19 increase by 4 19 to 23 increase by 4