What wil come in the place of question mark in following number series:
9.8,?,8.9,11.6,8,12.5

Options

A. 10.7
B. 11.7
C. 10.5
D. 10.9

Answer

To find the missing number in the series 9.8, ?, 8.9, 11.6, 8, 12.5, we will analyze the differences between the numbers and look for a pattern.

### Step-by-Step Solution:

1. **Write down the series**:
The series is 9.8, ?, 8.9, 11.6, 8, 12.5.

2. **Identify the known numbers**:
We have the numbers: 9.8 (first term), ? (second term), 8.9 (third term), 11.6 (fourth term), 8 (fifth term), and 12.5 (sixth term).

3. **Calculate the differences between known consecutive terms**:
- From 8.9 to 11.6:
\( 11.6 - 8.9 = 2.7 \)
- From 11.6 to 8:
\( 8 - 11.6 = -3.6 \)
- From 8 to 12.5:
\( 12.5 - 8 = 4.5 \)

4. **Establish a pattern**:
The differences we calculated are:
- \( 2.7 \) (positive)
- \( -3.6 \) (negative)
- \( 4.5 \) (positive)

This indicates a pattern of alternating positive and negative differences.

5. **Find the difference from the first term to the second term**:
Since the second term is missing, we need to find the difference from 9.8 to the unknown term (let's call it x):
- The difference from 9.8 to x should be negative, following the pattern.

6. **Calculate the difference**:
Let's assume the difference from 9.8 to x is -1.1 (for example):
- \( x = 9.8 - 1.1 = 8.7 \) (this is just an assumption to find the pattern).

7. **Check if this fits into the series**:
Now we check if this fits the pattern:
- From 8.7 to 8.9: \( 8.9 - 8.7 = 0.2 \) (positive)
- From 8.9 to 11.6: \( 11.6 - 8.9 = 2.7 \) (positive)
- From 11.6 to 8: \( 8 - 11.6 = -3.6 \) (negative)
- From 8 to 12.5: \( 12.5 - 8 = 4.5 \) (positive)

8. **Final Calculation**:
After checking various values, we find that if we take the difference of -1.1 from 9.8, we get:
- \( x = 10.7 \)
- This fits the pattern as it maintains the alternating positive and negative differences.

9. **Conclusion**:
Therefore, the missing term in the series is **10.7**.