93 95 98 ? 110 121 134

Options

A. 104
B. 96
C. 82
D. 103

Explanation

To find the missing number in the series 93, 95, 98, ?, 110, 121, 134, we will analyze the differences between the numbers and identify a pattern.

### Step-by-Step Solution:

1. **Identify the given series**:
The series is: 93, 95, 98, ?, 110, 121, 134.

2. **Calculate the differences between consecutive numbers**:
- Difference between 95 and 93:
\[ 95 - 93 = 2 \]
- Difference between 98 and 95:
\[ 98 - 95 = 3 \]
- Difference between 110 and 98:
\[ 110 - 98 = 12 \]
- Difference between 121 and 110:
\[ 121 - 110 = 11 \]
- Difference between 134 and 121:
\[ 134 - 121 = 13 \]

3. **List the differences**:
The differences we have so far are: 2, 3, ?, 12, 11, 13.

4. **Identify the pattern in the differences**:
The differences seem to follow a pattern of prime numbers:
- The first difference is 2 (the first prime number).
- The second difference is 3 (the second prime number).
- The next prime number after 3 is 5, which we suspect is the missing difference.
- Then we have 11 (the fifth prime number) and 13 (the sixth prime number).

5. **Calculate the missing number**:
- To find the missing number, we add the prime number 5 to the last known number in the series, which is 98:
\[ 98 + 5 = 103 \]

6. **Verify the series**:
- Now, let's check if the series holds:
- 93 + 2 = 95
- 95 + 3 = 98
- 98 + 5 = 103
- 103 + 7 = 110
- 110 + 11 = 121
- 121 + 13 = 134
- The series is consistent with the identified pattern.

7. **Conclusion**:
The missing number in the series is **103**.