3,10,21,36,55,70 ,105

Options

A. 105
B. 70
C. 36
D. 55

Answer

To find the odd number out in the series 3, 10, 21, 36, 55, 70, 105, we will analyze the pattern of differences between consecutive terms.

### Step-by-Step Solution:

1. **List the series**:
We start with the given series:
\[ 3, 10, 21, 36, 55, 70, 105 \]

2. **Calculate the differences between consecutive terms**:
- \(10 - 3 = 7\)
- \(21 - 10 = 11\)
- \(36 - 21 = 15\)
- \(55 - 36 = 19\)
- \(70 - 55 = 15\)
- \(105 - 70 = 35\)

So, the differences are:
\[ 7, 11, 15, 19, 15, 35 \]

3. **Analyze the differences**:
The differences we calculated are:
- \(7\)
- \(11\)
- \(15\)
- \(19\)
- \(15\)
- \(35\)

We can see that the differences are not consistent. Let's look for a pattern:
- The first four differences (7, 11, 15, 19) are increasing by 4.
- However, the fifth difference (15) does not follow the pattern and is repeated.
- The last difference (35) is significantly larger than the previous differences.

4. **Identify the odd number**:
Given the inconsistencies in the differences, we can conclude that the number 70 does not fit the pattern established by the other numbers in the series.

5. **Final conclusion**:
Therefore, the odd number out in the series is:
\[ \boxed{70} \]