complete the following series
5, 7, 10, 15, 22, ….

Options

A. 31
B. 32
C. 38
D. 33

Explanation

To complete the series 5, 7, 10, 15, 22, we need to identify the pattern in the sequence. Let's break it down step by step.

### Step 1: Identify the Differences
First, we will find the differences between consecutive terms in the series.

- From 5 to 7:
\( 7 - 5 = 2 \)

- From 7 to 10:
\( 10 - 7 = 3 \)

- From 10 to 15:
\( 15 - 10 = 5 \)

- From 15 to 22:
\( 22 - 15 = 7 \)

So, the differences are:
2, 3, 5, 7.

### Step 2: Identify the Pattern in Differences
Now, let's analyze the differences we found:
- The differences are: 2, 3, 5, 7.

These numbers are all prime numbers. The next prime number after 7 is 11.

### Step 3: Add the Next Prime Number
Now, we will add the next prime number (11) to the last term in the series (22).

- \( 22 + 11 = 33 \)

### Conclusion
Thus, the next term in the series is **33**.