What should come in place of the question mark(?) in the following number series?
17 9 10 ? 35 90

Options

A. 21
B. `27cdot5`
C. 19
D. `16cdot5`

Answer

To solve the number series: 17, 9, 10, ?, 35, 90, we need to identify a pattern in the numbers.

### Step-by-Step Solution:

1. **Identify the pattern between the numbers:**
- The series starts with 17, then goes to 9, then to 10.
- We will look for a relationship between these numbers.

2. **Calculate the difference between consecutive numbers:**
- From 17 to 9: \( 17 - 9 = 8 \)
- From 9 to 10: \( 10 - 9 = 1 \)

3. **Look for a consistent pattern:**
- The first difference is -8 and the second difference is +1.
- We can see that the first number decreases significantly, while the second increases slightly.

4. **Continue the pattern:**
- If we assume a similar pattern continues, we can check the next number in the series.
- If we follow the pattern of alternating between a decrease and an increase, we can hypothesize that the next number after 10 will involve a decrease.

5. **Calculate the next number:**
- From 10, if we apply a similar decrease as we did from 17 to 9 (which was -8), we can try to find a reasonable decrease.
- However, we notice that the next number in the series is 35, which is a significant increase from the previous number.

6. **Check the next number in the series:**
- From 10 to 35, we can see that we are likely looking for a number that fits a pattern of multiplication or a different operation.
- Let's check if multiplying by a fraction or a specific number can help.

7. **Finding the missing number:**
- If we try to find a number that when multiplied by a certain factor gives us 35:
- We can try \( 10 \times 3.5 = 35 \).
- Thus, we can assume the missing number is \( 10 \times 1.5 = 15 \).

8. **Final check:**
- Now we check if the pattern holds:
- 17 to 9 (decrease by 8), 9 to 10 (increase by 1), 10 to 15 (increase by 5), and then 15 to 35 (increase by 20).
- This suggests a pattern of increasing differences.

9. **Conclusion:**
- The missing number in the series is **16.5**.

### Final Answer:
The number that should come in place of the question mark (?) is **16.5**.