What will come in place of question mark (?) in the following series?
1,3,6,10,15,?

Options

A. A)17
B. B)18
C. C)20
D. D)21

Explanation

To find the missing term in the series 1, 3, 6, 10, 15, ?, we will analyze the pattern in the series step by step.

### Step 1: Identify the series
The given series is:
1, 3, 6, 10, 15, ?

### Step 2: Find the differences between consecutive terms
Let's calculate the differences between each pair of consecutive terms:

- Difference between 3 and 1:
\( 3 - 1 = 2 \)

- Difference between 6 and 3:
\( 6 - 3 = 3 \)

- Difference between 10 and 6:
\( 10 - 6 = 4 \)

- Difference between 15 and 10:
\( 15 - 10 = 5 \)

Now, we can list the differences:
- 2, 3, 4, 5

### Step 3: Identify the pattern in the differences
We can see that the differences are increasing by 1 each time:
- 2 (1st difference)
- 3 (2nd difference)
- 4 (3rd difference)
- 5 (4th difference)

### Step 4: Predict the next difference
Following the established pattern, the next difference should be:
- 6 (5th difference)

### Step 5: Calculate the next term
Now we will add this difference to the last term in the series:
- Last term = 15
- Next difference = 6

So, we calculate:
\( 15 + 6 = 21 \)

### Conclusion
The missing term in the series is:
**21**