4,5,7,10,14,18,25,32

Options

A. 7
B. 14
C. 18
D. 32

Answer

To find the odd term in the series 4, 5, 7, 10, 14, 18, 25, 32, we will analyze the differences between consecutive terms and look for any irregularities.

### Step-by-Step Solution:

1. **List the Series**:
The given series is: 4, 5, 7, 10, 14, 18, 25, 32.

2. **Calculate the Differences**:
We will calculate the differences between consecutive terms:
- 5 - 4 = 1
- 7 - 5 = 2
- 10 - 7 = 3
- 14 - 10 = 4
- 18 - 14 = 4
- 25 - 18 = 7
- 32 - 25 = 7

This gives us the differences: 1, 2, 3, 4, 4, 7, 7.

3. **Analyze the Differences**:
Now, let's analyze the differences:
- The first four differences (1, 2, 3, 4) are consecutive integers.
- The next difference is 4, which is repeated.
- The next difference jumps to 7, which is also repeated.

4. **Identify the Odd Term**:
The pattern in the differences suggests that the series should continue with increasing differences. After 4, we would expect the next difference to be 5, not 4 again. Therefore, the term that follows 18 should be 18 + 5 = 23, not 25.

5. **Conclusion**:
Since 25 does not fit the expected pattern of differences, it is the odd term in the series.

### Final Answer:
The odd term in the series is **25**.

---