In each question, a. number series is given. Only one number is wrong which doesn’t fit in the series. Find out the wrong number
4 15 37 100 224 439 781

Options

A. 224
B. 100
C. 439
D. 15

Answer

To solve the problem of identifying the wrong number in the series: 4, 15, 37, 100, 224, 439, 781, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Pattern**:
Start by examining the numbers in the series to identify a potential pattern.

2. **Check the Squares**:
Notice that the first number, 4, can be expressed as \(1^2 + 3\).
- \(1^2 + 3 = 1 + 3 = 4\)

3. **Continue with the Next Numbers**:
- For 15: \(3^2 + 6 = 9 + 6 = 15\)
- For 37: \(6^2 + 1 = 36 + 1 = 37\)
- For 100: \(10^2 + 0 = 100 + 0 = 100\)
- For 224: \(15^2 - 1 = 225 - 1 = 224\)
- For 439: \(21^2 - 2 = 441 - 2 = 439\)
- For 781: \(28^2 - 3 = 784 - 3 = 781\)

4. **Identify the Sequence of Squares**:
The sequence of numbers whose squares we are using is:
- 1, 3, 6, 10, 15, 21, 28
These numbers are the triangular numbers, and they are increasing by 1, 2, 3, 4, 5, 6, 7 respectively.

5. **Check the Differences**:
The differences between the squares and the added/subtracted numbers are:
- For 4: \(1^2 + 3\) (3)
- For 15: \(3^2 + 6\) (6)
- For 37: \(6^2 + 1\) (1)
- For 100: \(10^2 + 0\) (0)
- For 224: \(15^2 - 1\) (-1)
- For 439: \(21^2 - 2\) (-2)
- For 781: \(28^2 - 3\) (-3)

6. **Identify the Anomaly**:
The pattern of the added/subtracted numbers is inconsistent. The number 15 does not fit the pattern as it should be 11 based on the triangular number pattern.

7. **Conclusion**:
Therefore, the wrong number in the series is **15**.