2, 3, 5, 8, 13, 21, ….

Options

A. 29
B. 30
C. 32
D. 34

Explanation

To find the missing number in the series 2, 3, 5, 8, 13, 21, we will analyze the pattern in the series step by step.

### Step 1: Identify the series
The given series is: 2, 3, 5, 8, 13, 21.

### Step 2: Look for a pattern
We can observe how each number in the series relates to the previous numbers. Let's check the differences between consecutive terms:

- 3 - 2 = 1
- 5 - 3 = 2
- 8 - 5 = 3
- 13 - 8 = 5
- 21 - 13 = 8

### Step 3: Analyze the differences
The differences we calculated are: 1, 2, 3, 5, 8.

Now, let's look at the differences between these differences:
- 2 - 1 = 1
- 3 - 2 = 1
- 5 - 3 = 2
- 8 - 5 = 3

The second level of differences is: 1, 1, 2, 3.

### Step 4: Identify the next difference
We can see that the differences themselves are forming a pattern similar to the Fibonacci sequence:
- 1, 1, 2, 3, ...

Following this pattern, the next number in the difference sequence would be:
- 3 + 2 = 5

### Step 5: Calculate the next term in the original series
Now, we add this new difference (which is 5) to the last number in the original series (21):
- 21 + 13 = 34

### Conclusion
The next number in the series is **34**.