What will come in place of question mark (?) in the following number series?
23, 439, 647,751, 803, (?)

Options

A. 864
B. 819
C. 855
D. none of these

Answer

To find the missing number in the series: 23, 439, 647, 751, 803, (?), we will analyze the pattern of differences between consecutive numbers.

### Step-by-Step Solution:

1. **Identify the first two numbers:**
- The first number is 23.
- The second number is 439.

2. **Calculate the difference between the first two numbers:**
\[ 439 - 23 = 416 \]
- So, the first difference is 416.

3. **Identify the second and third numbers:**
- The second number is 439.
- The third number is 647.

4. **Calculate the difference between the second and third numbers:**
\[ 647 - 439 = 208 \]
- The second difference is 208.

5. **Identify the third and fourth numbers:**
- The third number is 647.
- The fourth number is 751.

6. **Calculate the difference between the third and fourth numbers:**
\[ 751 - 647 = 104 \]
- The third difference is 104.

7. **Identify the fourth and fifth numbers:**
- The fourth number is 751.
- The fifth number is 803.

8. **Calculate the difference between the fourth and fifth numbers:**
\[ 803 - 751 = 52 \]
- The fourth difference is 52.

9. **Observe the pattern in the differences:**
- The differences are: 416, 208, 104, 52.
- Each difference is half of the previous difference.

10. **Calculate the next difference:**
- The next difference would be half of 52:
\[ \frac{52}{2} = 26 \]

11. **Add this difference to the last number in the series:**
- The last number is 803.
\[ 803 + 26 = 829 \]

12. **Conclusion:**
- Therefore, the missing number in the series is 829.

### Final Answer:
The number that comes in place of the question mark (?) is **829**.

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