complete the following series
11, 23, 48, 99, 202, ….

Options

A. 409
B. 408
C. 407
D. 406

Explanation

To solve the series completion problem, we need to analyze the given sequence:

**Given Series:** 11, 23, 48, 99, 202, …

### Step 1: Identify the Pattern
First, we observe how the numbers are changing. We can see that the series is increasing, and we can try to find a pattern by examining the relationship between consecutive terms.

### Step 2: Calculate the Differences
Let's calculate the differences between consecutive terms:

- \( 23 - 11 = 12 \)
- \( 48 - 23 = 25 \)
- \( 99 - 48 = 51 \)
- \( 202 - 99 = 103 \)

So, the differences are: 12, 25, 51, 103.

### Step 3: Analyze the Differences
Next, let's look at the differences between these differences:

- \( 25 - 12 = 13 \)
- \( 51 - 25 = 26 \)
- \( 103 - 51 = 52 \)

The second differences are: 13, 26, 52.

### Step 4: Analyze the Second Differences
Now, let's look at the differences between the second differences:

- \( 26 - 13 = 13 \)
- \( 52 - 26 = 26 \)

The third differences are: 13, 26.

### Step 5: Identify the Pattern in the Third Differences
The third differences are increasing by a factor of 2. This suggests that the next difference in the second differences could be \( 52 + 52 = 104 \).

### Step 6: Calculate the Next Second Difference
Now, we add this to the last second difference:

- Next second difference: \( 103 + 104 = 207 \)

### Step 7: Calculate the Next First Difference
Now we can calculate the next first difference:

- Next first difference: \( 202 + 207 = 409 \)

### Step 8: Final Calculation
Finally, we can find the next term in the series:

- Next term: \( 202 + 409 = 611 \)

Thus, the completed series is: **11, 23, 48, 99, 202, 611.**

### Final Answer
The next term in the series is **611**.

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