What wil come in the place of question mark in following number series:
12,?,6,9,18,45

Options

A. A)15
B. B)8
C. C)6
D. D)12

Answer

To find the missing term in the series: 12, ?, 6, 9, 18, 45, we will analyze the pattern in the series step by step.

### Step 1: Identify the known terms
The series is: 12, ?, 6, 9, 18, 45. The first term is 12, the third term is 6, the fourth term is 9, the fifth term is 18, and the sixth term is 45.

### Step 2: Look for a pattern in the series
We will check how each term relates to the next one.

- From 6 to 9:
\[ 6 \times 1.5 = 9 \]

- From 9 to 18:
\[ 9 \times 2 = 18 \]

- From 18 to 45:
\[ 18 \times 2.5 = 45 \]

### Step 3: Determine the multiplication pattern
We can see that the multiplication factors are:
- From 6 to 9: multiplied by 1.5
- From 9 to 18: multiplied by 2
- From 18 to 45: multiplied by 2.5

The multiplication factors are increasing by 0.5 each time.

### Step 4: Work backwards to find the missing term
Now, we will work backwards to find the missing term (let's call it K) before 6:
- Before 6, we need to find the term that multiplied by some factor to give us 6.

If we assume that the factor before 6 was 1 (since we see the pattern starts at 1.5):
\[ K \times 1 = 6 \implies K = 6 \]

### Step 5: Check the first term with the identified pattern
Now, we need to check the term before K (which is 12):
- The factor to go from 12 to K should be 0.5:
\[ 12 \times 0.5 = 6 \]

### Conclusion
Thus, the missing term in the series is **6**.

### Final Answer
The answer is **6**.

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