3 5 8 13 21 34 ?

Options

A. 62
B. 57
C. 55
D. 74

Explanation

To find the next number in the series 3, 5, 8, 13, 21, 34, we can follow these steps:

### Step 1: Identify the Series
The given series is:
3, 5, 8, 13, 21, 34

### Step 2: Find the Differences
Let's calculate the differences between consecutive terms:
- 5 - 3 = 2
- 8 - 5 = 3
- 13 - 8 = 5
- 21 - 13 = 8
- 34 - 21 = 13

So, the differences are:
2, 3, 5, 8, 13

### Step 3: Analyze the Differences
Now, let's look at the differences we calculated:
2, 3, 5, 8, 13

We can see that these differences themselves form a series. Let's find the differences of these differences:
- 3 - 2 = 1
- 5 - 3 = 2
- 8 - 5 = 3
- 13 - 8 = 5

The second differences are:
1, 2, 3, 5

### Step 4: Identify the Pattern in the Differences
The differences of the differences (1, 2, 3, 5) also seem to follow a pattern. They appear to be the Fibonacci sequence, where each number is the sum of the two preceding ones:
- 1 + 2 = 3
- 2 + 3 = 5

### Step 5: Calculate the Next Difference
Continuing the Fibonacci pattern, the next number after 5 would be:
3 + 5 = 8

### Step 6: Find the Next Term in the Original Series
Now, we add the last difference (which is 13) to the last term of the original series (which is 34):
34 + 21 = 55

### Conclusion
Thus, the next number in the series is **55**.