What will come in place of question mark in following number series 60 62 64 70 100 310 ?

Options

A. 1800
B. 2000
C. 2100
D. 2200

Answer

To solve the number series: 60, 62, 64, 70, 100, 310, ?, we will analyze the pattern of differences between the numbers.

### Step-by-Step Solution:

1. **Identify the series**: The given series is 60, 62, 64, 70, 100, 310.

2. **Calculate the differences between consecutive terms**:
- 62 - 60 = 2
- 64 - 62 = 2
- 70 - 64 = 6
- 100 - 70 = 30
- 310 - 100 = 210

So, the differences are: 2, 2, 6, 30, 210.

3. **Analyze the differences**:
- The first two differences are 2 (2, 2).
- The third difference is 6, which can be seen as 2 multiplied by 3.
- The fourth difference is 30, which can be seen as 6 multiplied by 5.
- The fifth difference is 210, which can be seen as 30 multiplied by 7.

This suggests a pattern where each difference is derived from the previous difference multiplied by an increasing odd number:
- 2 (1st difference)
- 2 (2nd difference)
- 2 * 3 = 6 (3rd difference)
- 6 * 5 = 30 (4th difference)
- 30 * 7 = 210 (5th difference)

4. **Predict the next difference**:
- Following the pattern, the next difference should be 210 multiplied by 9 (the next odd number).
- 210 * 9 = 1890.

5. **Calculate the next term in the series**:
- To find the term that comes after 310, we add the predicted difference (1890) to 310.
- 310 + 1890 = 2200.

6. **Final answer**:
- The number that will come in place of the question mark is **2200**.