950 661 436 269 146 65 16

Options

A. 436
B. 65
C. 269
D. 661

Explanation

To find the wrong number in the series: 950, 661, 436, 269, 146, 65, 16, we will analyze the differences between consecutive numbers and identify a pattern.

### Step-by-Step Solution:

1. **Identify the Series**:
The series given is:
\[ 950, 661, 436, 269, 146, 65, 16 \]

2. **Calculate the Differences**:
We will find the differences between consecutive numbers:
- \( 950 - 661 = 289 \)
- \( 661 - 436 = 225 \)
- \( 436 - 269 = 167 \)
- \( 269 - 146 = 123 \)
- \( 146 - 65 = 81 \)
- \( 65 - 16 = 49 \)

The differences are:
\[ 289, 225, 167, 123, 81, 49 \]

3. **Identify the Pattern**:
Now, we will check if these differences follow a specific pattern.
- \( 289 = 17^2 \)
- \( 225 = 15^2 \)
- \( 167 \) does not appear to be a perfect square.
- \( 123 = 11^2 + 2 \)
- \( 81 = 9^2 \)
- \( 49 = 7^2 \)

We notice that the differences are supposed to be perfect squares of odd numbers in descending order:
- \( 17^2, 15^2, 13^2, 11^2, 9^2, 7^2 \)

4. **Determine the Incorrect Number**:
Since \( 167 \) is not a perfect square, we can conclude that the number before \( 146 \) is incorrect. The correct difference should be \( 13^2 = 169 \).

5. **Calculate the Correct Number**:
If the correct difference is \( 169 \), then the number before \( 146 \) should be:
\[ 269 - 169 = 100 \]

6. **Conclusion**:
Therefore, the wrong number in the series is \( 146 \) and it should be replaced with \( 100 \).

### Final Answer:
The wrong number in the series is **146**, and it should be **100**.

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