What will come in place of question mark (?) in the following number series?
`13 ,52,29,68,45,(?)`

Options

A. 97
B. 74
C. 84
D. 76

Answer

To solve the number series: `13, 52, 29, 68, 45, (?)`, we can break it down into two separate sequences based on the position of the numbers:

1. **First Sequence (Odd Position):**
- The numbers in the odd positions are: 13, 29, 45
- The differences between these numbers can be calculated as follows:
- 29 - 13 = 16
- 45 - 29 = 16
- This indicates that the odd-position numbers are increasing by 16 each time.

2. **Second Sequence (Even Position):**
- The numbers in the even positions are: 52, 68, (?)
- The difference between these numbers can be calculated as follows:
- 68 - 52 = 16
- This indicates that the even-position numbers are also increasing by 16.

Now, we can find the missing number in the series:

- For the odd-position sequence:
- The next number after 45 would be:
- 45 + 16 = 61

- For the even-position sequence:
- The next number after 68 would be:
- 68 + 16 = 84

Thus, the complete series looks like this:
- Odd positions: 13, 29, 45, 61
- Even positions: 52, 68, 84

Therefore, the number that comes in place of the question mark (?) is **84**.

### Steps Summary:
1. Identify the odd and even positioned numbers in the series.
2. Calculate the differences in the odd-position numbers (16).
3. Calculate the differences in the even-position numbers (16).
4. Add 16 to the last even-position number (68) to find the missing number (84).