What will come in place of the question mark (?) in the following number series?
`12" "12" "18" "45" "180" "1170`

Options

A. 12285
B. 10530
C. 11700
D. 12870

Answer

To find the missing term in the series `12, 12, 18, 45, 180, 1170, ?`, we will analyze the pattern of the series step by step.

### Step 1: Identify the series
The series is:
- 12, 12, 18, 45, 180, 1170

### Step 2: Look for a pattern
We can observe the following:
- The first two terms are the same: 12 and 12.
- The third term is 18, which is derived from the second term (12).

### Step 3: Calculate the multiplication factors
1. From the first term (12) to the second term (12):
- \( 12 \times 1 = 12 \)

2. From the second term (12) to the third term (18):
- \( 12 \times 1.5 = 18 \)

3. From the third term (18) to the fourth term (45):
- \( 18 \times 2.5 = 45 \)

4. From the fourth term (45) to the fifth term (180):
- \( 45 \times 4 = 180 \)

5. From the fifth term (180) to the sixth term (1170):
- \( 180 \times 6.5 = 1170 \)

### Step 4: Identify the pattern in multiplication factors
The multiplication factors we used are:
- 1 (for the first to second term)
- 1.5 (for the second to third term)
- 2.5 (for the third to fourth term)
- 4 (for the fourth to fifth term)
- 6.5 (for the fifth to sixth term)

### Step 5: Determine the next multiplication factor
The pattern of the multiplication factors appears to be increasing:
- 1, 1.5, 2.5, 4, 6.5

The differences between these factors are:
- \(1.5 - 1 = 0.5\)
- \(2.5 - 1.5 = 1\)
- \(4 - 2.5 = 1.5\)
- \(6.5 - 4 = 2.5\)

The differences are increasing by 0.5, 1, 1.5, and 2.5. The next difference could be assumed to be 4 (continuing the pattern of increasing differences).

### Step 6: Calculate the next multiplication factor
Adding 4 to the last multiplication factor (6.5):
- \(6.5 + 4 = 10.5\)

### Step 7: Calculate the next term
Now, we will multiply the last term (1170) by the next multiplication factor (10.5):
- \(1170 \times 10.5 = 12285\)

### Conclusion
Thus, the term that will come in place of the question mark (?) is **12285**.