The sixth term of the sequence 2 , 6 , 11 , 17 , …..is

Options

A. 24
B. 30
C. 32
D. 36

Answer

To find the sixth term of the sequence 2, 6, 11, 17, we will first identify the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Sequence**: The given sequence is 2, 6, 11, 17.

2. **Calculate the Differences**:
- First, find the difference between consecutive terms:
- 6 - 2 = 4
- 11 - 6 = 5
- 17 - 11 = 6
- So, the differences are: 4, 5, 6.

3. **Identify the Pattern in Differences**:
- The differences are increasing by 1 each time (4, 5, 6).
- This suggests that the next difference will be 7.

4. **Find the 5th Term**:
- To find the 5th term, add the next difference (7) to the last known term (17):
- 17 + 7 = 24.
- Therefore, the 5th term is 24.

5. **Find the 6th Term**:
- Now, to find the 6th term, we add the next difference (which is now 8) to the 5th term (24):
- 24 + 8 = 32.
- Therefore, the 6th term is 32.

### Conclusion:
The sixth term of the sequence is **32**.