What will come in place of the question mark (?) in thee following number series?
2 15 41 80 132 ?

Options

A. 197
B. 150
C. 178
D. 180

Answer

To find the missing number in the series 2, 15, 41, 80, 132, ?, we need to analyze the differences between the consecutive terms.

1. **Calculate the differences between the terms:**
- 15 - 2 = 13
- 41 - 15 = 26
- 80 - 41 = 39
- 132 - 80 = 52

So, the differences are: 13, 26, 39, 52.

2. **Identify the pattern in the differences:**
- The differences themselves are increasing:
- 26 - 13 = 13
- 39 - 26 = 13
- 52 - 39 = 13

This shows that the differences are increasing by 13 each time.

3. **Calculate the next difference:**
- The next difference after 52 would be:
- 52 + 13 = 65

4. **Add the next difference to the last term in the series:**
- The last term we have is 132.
- Now we add the next difference:
- 132 + 65 = 197

Thus, the number that will come in place of the question mark (?) is **197**.

### Summary of Steps:
1. Calculate the differences between consecutive terms.
2. Identify the pattern in the differences.
3. Calculate the next difference based on the identified pattern.
4. Add the next difference to the last term to find the missing number.