Find the value of (?) in the following number series.
`150," "152," "157," "167," "184," "?`

Options

A. A)229
B. B)245
C. C)232
D. D)210

Answer

To find the value of (?) in the given number series: `150, 152, 157, 167, 184, ?`, we will analyze the differences between the consecutive terms and look for a pattern.

### Step-by-Step Solution:

1. **Identify the series**:
The series is:
- 150
- 152
- 157
- 167
- 184
- ?

2. **Calculate the first differences**:
We will find the difference between each pair of consecutive terms:
- 152 - 150 = 2
- 157 - 152 = 5
- 167 - 157 = 10
- 184 - 167 = 17

So, the first differences are:
- 2, 5, 10, 17

3. **Calculate the second differences**:
Now, we will find the difference between the first differences:
- 5 - 2 = 3
- 10 - 5 = 5
- 17 - 10 = 7

The second differences are:
- 3, 5, 7

4. **Identify the pattern in the second differences**:
The second differences are increasing:
- From 3 to 5, the increase is 2.
- From 5 to 7, the increase is also 2.

Following this pattern, the next second difference should be:
- 7 + 2 = 9

5. **Calculate the next first difference**:
Now, we will add this new second difference to the last first difference:
- Last first difference = 17
- Next first difference = 17 + 9 = 26

6. **Calculate the missing term**:
Finally, we will add this new first difference to the last term in the series:
- Last term = 184
- Next term = 184 + 26 = 210

Thus, the value of (?) is **210**.

### Summary:
The missing term in the series is **210**.