4 13 17 ? 30 39

Options

A. 29
B. 21
C. 26
D. 19

Explanation

To solve the series: 4, 13, 17, ?, 30, 39, we will identify the pattern by calculating the differences between the consecutive numbers.

### Step-by-Step Solution:

1. **Identify the series**: The given series is 4, 13, 17, ?, 30, 39.

2. **Calculate the differences between consecutive terms**:
- Difference between 13 and 4:
\[ 13 - 4 = 9 \]
- Difference between 17 and 13:
\[ 17 - 13 = 4 \]
- Difference between 30 and 17 (unknown term):
\[ 30 - ? = ? \]
- Difference between 39 and 30:
\[ 39 - 30 = 9 \]

3. **Establish the pattern**:
- We notice that the differences alternate between 9 and 4:
- 4 + 9 = 13
- 13 + 4 = 17
- 17 + 9 = ?
- ? + 4 = 30
- 30 + 9 = 39

4. **Calculate the missing term**:
- From the established pattern, we can find the missing term:
\[ 17 + 9 = 26 \]
- So, the missing number in the series is 26.

5. **Verify the next term**:
- Now, we check if adding 4 to the missing term gives us the next number:
\[ 26 + 4 = 30 \]
- This confirms that the pattern holds.

### Final Answer:
The missing number in the series is **26**.