What will come in place of question. Mark (?) in the following series questions?
12,36,80,164,328,?

Options

A. 648
B. 664
C. 660
D. 652

Answer

To solve the series: 12, 36, 80, 164, 328, ?, we need to identify the pattern in the differences between the numbers.

### Step-by-Step Solution:

1. **Identify the Series**:
The series given is: 12, 36, 80, 164, 328.

2. **Calculate the First Differences**:
- 36 - 12 = 24
- 80 - 36 = 44
- 164 - 80 = 84
- 328 - 164 = 164

So, the first differences are: 24, 44, 84, 164.

3. **Calculate the Second Differences**:
Now, let's find the differences of the first differences:
- 44 - 24 = 20
- 84 - 44 = 40
- 164 - 84 = 80

So, the second differences are: 20, 40, 80.

4. **Calculate the Third Differences**:
Now, let's find the differences of the second differences:
- 40 - 20 = 20
- 80 - 40 = 40

So, the third differences are: 20, 40.

5. **Identify the Pattern**:
The third differences are increasing by a factor of 2:
- 20 (doubled becomes) 40.

If we continue this pattern, the next difference would be:
- 40 (doubled becomes) 80.

6. **Find the Next Second Difference**:
The next second difference would be:
- 80 + 80 = 160.

7. **Find the Next First Difference**:
The next first difference would be:
- 164 + 160 = 324.

8. **Find the Next Number in the Series**:
Finally, add this first difference to the last number in the series:
- 328 + 324 = 652.

Thus, the number that will come in place of the question mark (?) is **652**.