What will come in place of question mark (?) in the following series questions?
6,36,180,720,?,4320

Options

A. A)3600
B. B)1080
C. C)1440
D. D)2160

Answer

To find the missing term in the series: 6, 36, 180, 720, ?, 4320, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
We will look at how each term relates to the previous term.

- The first term is 6.
- The second term is 36.
- The third term is 180.
- The fourth term is 720.
- The fifth term is unknown (let's denote it as K).
- The sixth term is 4320.

### Step 2: Calculate the multipliers
Now, let's find out how each term is derived from the previous one:

1. From 6 to 36:
\[ 6 \times 6 = 36 \]
(Here, we multiplied by 6)

2. From 36 to 180:
\[ 36 \times 5 = 180 \]
(Here, we multiplied by 5)

3. From 180 to 720:
\[ 180 \times 4 = 720 \]
(Here, we multiplied by 4)

### Step 3: Determine the next multiplier
Following this pattern, we see that the multipliers are decreasing by 1 each time:
- First multiplier: 6
- Second multiplier: 5
- Third multiplier: 4
- Fourth multiplier: 3 (for the next term)

### Step 4: Calculate the missing term (K)
Now, we will use the fourth multiplier (3) to find K:
\[ K = 720 \times 3 = 2160 \]

### Step 5: Verify the last term
To ensure our answer is correct, we can check if multiplying K by the next multiplier (which would be 2) gives us the last term:
\[ 4320 = 2160 \times 2 \]
This confirms that our calculation is correct.

### Conclusion
The missing term in the series is:
\[ \boxed{2160} \]