What should come in place of the question mark(?) in the following number series?
3 20 78 332 1680 ?

Options

A. 8410
B. 9836
C. 10098
D. 1150

Answer

To find the missing number in the series: 3, 20, 78, 332, 1680, ?, we need to identify a pattern or a rule that governs the progression of the numbers.

### Step-by-step Solution:

1. **Identify the pattern**: Let's look at the ratios or the differences between consecutive terms to see if we can find a pattern.

- From 3 to 20:
\[ 20 = 3 \times 6 + 2 \]
- From 20 to 78:
\[ 78 = 20 \times 3 + 18 \]
- From 78 to 332:
\[ 332 = 78 \times 4 + 20 \]
- From 332 to 1680:
\[ 1680 = 332 \times 5 + 10 \]

2. **Observe the multipliers and additions**:
- The multipliers seem to increase by 1 each time (6, 3, 4, 5).
- The additions also seem to follow a pattern: 2, 18, 20, 10.

3. **Finding the next term**:
- Following the pattern, the next term after 1680 should be obtained by multiplying 1680 by 6 and adding a certain number.
- Let's assume the addition follows a pattern. The differences in the additions are:
- 18 - 2 = 16
- 20 - 18 = 2
- 10 - 20 = -10

This doesn't seem to follow a clear pattern. However, if we continue with the multiplier:
\[ ? = 1680 \times 6 + 0 \]

4. **Calculate the next term**:
\[ ? = 1680 \times 6 = 10080 \]

### Conclusion:
The missing number in the series is **10080**.