13 13 19 43 103 ?

Options

A. 221
B. 227
C. 223
D. 217

Explanation

To find the next number in the series: 13, 13, 19, 43, 103, we will analyze the differences between the consecutive terms and look for a pattern.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is 13, 13, 19, 43, 103.

2. **Calculate the Differences**:
- The difference between the first two terms (13 and 13) is:
\[ 13 - 13 = 0 \]
- The difference between the second and third terms (13 and 19) is:
\[ 19 - 13 = 6 \]
- The difference between the third and fourth terms (19 and 43) is:
\[ 43 - 19 = 24 \]
- The difference between the fourth and fifth terms (43 and 103) is:
\[ 103 - 43 = 60 \]

So, the differences are: 0, 6, 24, 60.

3. **Calculate the Differences of Differences**:
- The difference between the first two differences (0 and 6) is:
\[ 6 - 0 = 6 \]
- The difference between the second and third differences (6 and 24) is:
\[ 24 - 6 = 18 \]
- The difference between the third and fourth differences (24 and 60) is:
\[ 60 - 24 = 36 \]

So, the second-level differences are: 6, 18, 36.

4. **Calculate the Differences of Second-Level Differences**:
- The difference between the first two second-level differences (6 and 18) is:
\[ 18 - 6 = 12 \]
- The difference between the second and third second-level differences (18 and 36) is:
\[ 36 - 18 = 18 \]

So, the third-level differences are: 12, 18.

5. **Identify the Pattern**:
- The differences of the second-level differences seem to increase by 6 (12 to 18). We can predict the next difference will be:
\[ 18 + 6 = 24 \]

6. **Calculate the Next Second-Level Difference**:
- Adding this to the last second-level difference:
\[ 36 + 24 = 60 \]

7. **Calculate the Next First-Level Difference**:
- Adding this to the last first-level difference:
\[ 60 + 60 = 120 \]

8. **Calculate the Next Term in the Series**:
- Adding this to the last term (103):
\[ 103 + 120 = 223 \]

Thus, the next number in the series is **223**.