complete the series
23, 48, 99, 203, 413, ….

Options

A. 927
B. 837
C. 937
D. 437

Explanation

To complete the series 23, 48, 99, 203, 413, …, we will analyze the pattern in the series step by step.

### Step 1: Observe the series
The series is:
23, 48, 99, 203, 413

### Step 2: Find the differences
Let's calculate the differences between consecutive terms:
- 48 - 23 = 25
- 99 - 48 = 51
- 203 - 99 = 104
- 413 - 203 = 210

So, the differences are:
25, 51, 104, 210

### Step 3: Find the differences of the differences
Now, let's find the differences of these differences:
- 51 - 25 = 26
- 104 - 51 = 53
- 210 - 104 = 106

So, the second level differences are:
26, 53, 106

### Step 4: Find the differences of the second differences
Next, we calculate the differences of the second differences:
- 53 - 26 = 27
- 106 - 53 = 53

So, the third level differences are:
27, 53

### Step 5: Analyze the pattern
Now, we notice that the first differences are increasing rapidly. Let's analyze the pattern in the first differences:
- The first differences (25, 51, 104, 210) appear to be increasing by a pattern that can be related to prime numbers.

### Step 6: Identify the prime numbers
The prime numbers we see in the differences are:
- The differences between the first differences are: 26 (which is not prime), 53 (which is prime), and 106 (which is not prime).

However, if we look at the prime numbers themselves, we can see:
- The differences between the terms seem to be increasing by prime numbers: 2, 3, 5, 7...

### Step 7: Continue the pattern
The next prime number after 7 is 11.
So, if we add 11 to the last difference (210):
- 210 + 11 = 221

### Step 8: Calculate the next term
Now, we add this new difference (221) to the last term in the original series (413):
- 413 + 221 = 634

### Conclusion
Thus, the next term in the series is **634**.