What will come in place of question mark (?) in the following series questions?
20,?,12,19,39,98.5

Options

A. A)9
B. B)10
C. C)11
D. D)24

Answer

To find the missing term in the series 20, ?, 12, 19, 39, 98.5, we will analyze the pattern in the sequence step by step.

### Step 1: Identify the known terms
The series is:
- 1st term: 20
- 2nd term: ?
- 3rd term: 12
- 4th term: 19
- 5th term: 39
- 6th term: 98.5

### Step 2: Look for a pattern
We will examine the relationship between the known terms to identify a pattern.

1. From the 3rd term (12) to the 4th term (19):
- 12 multiplied by 1.5 gives us 18, and then adding 1 results in 19.

2. From the 4th term (19) to the 5th term (39):
- 19 multiplied by 2 gives us 38, and then adding 1 results in 39.

3. From the 5th term (39) to the 6th term (98.5):
- 39 multiplied by 2.5 gives us 97.5, and then adding 1 results in 98.5.

### Step 3: Establish the multiplication pattern
We can see that the multiplication factor increases by 0.5 each time:
- 1.5 (for 12 to 19)
- 2.0 (for 19 to 39)
- 2.5 (for 39 to 98.5)

### Step 4: Apply the pattern to find the missing term
Now, we need to find the 2nd term (?). We know that:
- The 1st term (20) multiplied by a certain factor (which we need to determine) plus 1 should give us the 3rd term (12).

Let’s denote the missing term as K. The relationship can be expressed as:
\[ K \times 1 + 1 = 12 \]

### Step 5: Solve for K
From the equation:
\[ K + 1 = 12 \]
Subtracting 1 from both sides gives:
\[ K = 12 - 1 \]
\[ K = 11 \]

### Conclusion
The missing term in the series is **11**.