The wrong number of the sequence 36, 81, 144, 225, 256 441 is

Options

A. 36
B. 81
C. 225
D. 256

Answer

To identify the wrong number in the sequence 36, 81, 144, 225, 256, 441, we will analyze the pattern of the numbers.

### Step-by-Step Solution:

1. **Identify the Numbers**: The given sequence is 36, 81, 144, 225, 256, 441.

2. **Find the Square Roots**: Calculate the square roots of each number:
- √36 = 6
- √81 = 9
- √144 = 12
- √225 = 15
- √256 = 16
- √441 = 21

3. **List the Square Roots**: The square roots form the sequence: 6, 9, 12, 15, 16, 21.

4. **Identify the Pattern**: Observe the differences between consecutive numbers:
- 9 - 6 = 3
- 12 - 9 = 3
- 15 - 12 = 3
- 16 - 15 = 1 (This is where the pattern breaks)
- 21 - 16 = 5

5. **Determine the Expected Value**: Following the established pattern, after 15 (which is 12 squared), we should have:
- 15 + 3 = 18
- Therefore, the next number should be 18² = 324.

6. **Identify the Wrong Number**: Since 256 (16²) does not fit the pattern, it is the wrong number in the sequence. The correct number should be 324.

### Conclusion:
The wrong number in the sequence is **256**.

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