What should come in place of question mark (?) in the given number series ?
17, 18.6, 15.4, 21.8, 9, ?

Options

A. 34.8
B. 34.6
C. 32.2
D. 36.2

Answer

To find the missing number in the series: 17, 18.6, 15.4, 21.8, 9, ?, we will analyze the pattern of the series step by step.

### Step-by-Step Solution:

1. **Identify the first two numbers:**
- Start with the first number: 17.
- The second number is 18.6.
- To find the difference:
\[ 18.6 - 17 = 1.6 \]
- **Hint:** Look for the operation (addition or subtraction) between consecutive numbers.

2. **Identify the next operation:**
- The third number is 15.4.
- To find the difference from the second number:
\[ 15.4 - 18.6 = -3.2 \]
- **Hint:** Note that we are now subtracting a value.

3. **Continue the pattern:**
- The fourth number is 21.8.
- To find the difference from the third number:
\[ 21.8 - 15.4 = 6.4 \]
- **Hint:** We are adding again.

4. **Next operation:**
- The fifth number is 9.
- To find the difference from the fourth number:
\[ 9 - 21.8 = -12.8 \]
- **Hint:** We are subtracting again.

5. **Identify the pattern:**
- The differences we have are:
- +1.6 (add)
- -3.2 (subtract)
- +6.4 (add)
- -12.8 (subtract)
- We can see that the additions and subtractions are alternating.
- The absolute values of the differences are:
- 1.6, 3.2, 6.4, 12.8
- Notice that each subsequent number is double the previous one:
- \(1.6 \times 2 = 3.2\)
- \(3.2 \times 2 = 6.4\)
- \(6.4 \times 2 = 12.8\)

6. **Calculate the next addition:**
- The next difference should be:
\[ 12.8 \times 2 = 25.6 \]
- Since the last operation was subtraction, we will now add this value to the last number in the series (9):
\[ 9 + 25.6 = 34.6 \]

### Conclusion:
The missing number in the series is **34.6**.