`121,144,169,196,225,?`

Options

A. 289
B. 257
C. 256
D. 125

Answer

To solve the number series `121, 144, 169, 196, 225, ?`, we will analyze the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Numbers**: The given numbers are 121, 144, 169, 196, and 225.

2. **Find the Square Roots**:
- The square root of 121 is 11 (since \(11^2 = 121\)).
- The square root of 144 is 12 (since \(12^2 = 144\)).
- The square root of 169 is 13 (since \(13^2 = 169\)).
- The square root of 196 is 14 (since \(14^2 = 196\)).
- The square root of 225 is 15 (since \(15^2 = 225\)).

3. **Observe the Pattern**:
- The square roots of the numbers are consecutive integers: 11, 12, 13, 14, 15.
- This indicates that the next number in the series should be the square of the next consecutive integer, which is 16.

4. **Calculate the Next Number**:
- The square of 16 is \(16^2 = 256\).

5. **Conclusion**:
- Therefore, the next number in the series is 256.

### Final Answer:
The next number in the series is **256**.

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