Series 3, 4, 6, 9, 13, ... the next term is :

Options

A. 18
B. 17
C. 14
D. 19

Answer

To find the next term in the series 3, 4, 6, 9, 13, we can analyze the pattern of the differences between the terms.

**Step 1: Identify the series.**
The given series is:
3, 4, 6, 9, 13

**Step 2: Calculate the differences between consecutive terms.**
- The difference between 4 and 3 is:
4 - 3 = 1
- The difference between 6 and 4 is:
6 - 4 = 2
- The difference between 9 and 6 is:
9 - 6 = 3
- The difference between 13 and 9 is:
13 - 9 = 4

So, the differences between the terms are:
1, 2, 3, 4

**Step 3: Identify the pattern in the differences.**
The differences are increasing by 1 each time:
1, 2, 3, 4, ...

**Step 4: Predict the next difference.**
Following the pattern, the next difference should be:
4 + 1 = 5

**Step 5: Add the next difference to the last term of the series.**
Now, we add this difference to the last term in the series:
13 + 5 = 18

**Step 6: Conclusion.**
Thus, the next term in the series is:
18

**Final Answer: 18**

---