The sixth term of the sequence 11 ,13 ,17 ,19, 23, …..29 is

Options

A. 24
B. 19
C. 25
D. 22

Answer

To find the sixth term of the sequence 11, 13, 17, 19, 23, 29, we will analyze the pattern in the sequence step by step.

### Step 1: Identify the sequence
The given sequence is:
- 11, 13, 17, 19, 23, 29

### Step 2: Calculate the differences between consecutive terms
Let's find the differences between each term:
- 13 - 11 = 2
- 17 - 13 = 4
- 19 - 17 = 2
- 23 - 19 = 4
- 29 - 23 = 6

So, the differences are:
- 2, 4, 2, 4, 6

### Step 3: Look for a pattern in the differences
We can see that the differences alternate between adding 2 and adding 4, with an increase of 2 in the last difference:
- 2, 4, 2, 4, 6

### Step 4: Predict the next difference
Following the established pattern, after 6, we would expect to add 2 to get the next term:
- Next difference = 2 (after the last 6)

### Step 5: Calculate the sixth term
To find the sixth term, we add the next difference (which is 2) to the last known term (29):
- Sixth term = 29 + 2 = 31

### Conclusion
The sixth term of the sequence is 31.