What will come in place of (?) in the following number series problems?
`200," "197," "185," "163," "130," "?`

Options

A. A)95
B. B)85
C. C)105
D. D)86

Answer

To find the missing term in the series: 200, 197, 185, 163, 130, ?, we will analyze the differences between consecutive terms and identify a pattern.

### Step-by-Step Solution:

1. **Write down the series**:
The series is: 200, 197, 185, 163, 130, ?

2. **Calculate the differences between consecutive terms**:
- 200 - 197 = 3
- 197 - 185 = 12
- 185 - 163 = 22
- 163 - 130 = 33

So, the differences are: 3, 12, 22, 33.

3. **Identify the pattern in the differences**:
Now, let's look at the differences we calculated:
- The first difference is 3.
- The second difference is 12 (which is 3 + 9).
- The third difference is 22 (which is 12 + 10).
- The fourth difference is 33 (which is 22 + 11).

The differences between the differences are:
- 12 - 3 = 9
- 22 - 12 = 10
- 33 - 22 = 11

This shows that the second differences are increasing by 1 each time.

4. **Predict the next difference**:
Following the pattern, the next difference should be:
- 33 + 12 = 45 (since the last difference was 33, we add 12 to it).

5. **Calculate the missing term**:
Now, we subtract this new difference from the last known term (130):
- 130 - 45 = 85.

6. **Conclusion**:
Therefore, the missing term in the series is 85.

### Final Answer:
The missing term is **85**.