Numbers in the following series follow some rule. Find the missing term.
0, 5, 8, 17, 24, 37, 48, ?

Options

A. 59
B. 61
C. 63
D. 65

Answer

To find the missing term in the series 0, 5, 8, 17, 24, 37, 48, ?, we can analyze the pattern in the sequence step by step.

### Step-by-Step Solution:

1. **List the Given Series:**
The series is: 0, 5, 8, 17, 24, 37, 48, ?

2. **Identify the Pattern:**
Let's analyze the terms to find a relationship. We will look for a pattern in the differences between consecutive terms.

3. **Calculate the Differences:**
- Difference between 5 and 0: \( 5 - 0 = 5 \)
- Difference between 8 and 5: \( 8 - 5 = 3 \)
- Difference between 17 and 8: \( 17 - 8 = 9 \)
- Difference between 24 and 17: \( 24 - 17 = 7 \)
- Difference between 37 and 24: \( 37 - 24 = 13 \)
- Difference between 48 and 37: \( 48 - 37 = 11 \)

So, the differences are: 5, 3, 9, 7, 13, 11.

4. **Analyze the Differences:**
Now, let's look at the differences of the differences:
- Difference between 3 and 5: \( 3 - 5 = -2 \)
- Difference between 9 and 3: \( 9 - 3 = 6 \)
- Difference between 7 and 9: \( 7 - 9 = -2 \)
- Difference between 13 and 7: \( 13 - 7 = 6 \)
- Difference between 11 and 13: \( 11 - 13 = -2 \)

The second-level differences are: -2, 6, -2, 6, -2.

5. **Predict the Next Difference:**
Following the pattern of the second-level differences, the next difference should be 6 (since it alternates between -2 and 6).

6. **Calculate the Next Term:**
The last difference we calculated was 11 (from 48 to the next term). Therefore, we add 11 + 6 to get the next difference:
- Next difference: \( 11 + 6 = 17 \)

7. **Find the Missing Term:**
Now, we add this difference to the last term in the series:
- Missing term: \( 48 + 17 = 65 \)

### Conclusion:
The missing term in the series is **65**.