What should come in place of the question mark (?) in the following number series ?
`"3 ? 6 18 72 360 2160"`

Options

A. 4.5
B. 3
C. 4
D. 5.5

Answer

To find the missing number in the series `3, ?, 6, 18, 72, 360, 2160`, we will analyze the pattern of the series step by step.

### Step 1: Identify the pattern in the series
We can observe the numbers after the question mark: `6, 18, 72, 360, 2160`. Let's look at how each number relates to the previous one.

### Step 2: Calculate the ratios between consecutive terms
- From `6` to `18`:
\[ 18 = 6 \times 3 \]
- From `18` to `72`:
\[ 72 = 18 \times 4 \]
- From `72` to `360`:
\[ 360 = 72 \times 5 \]
- From `360` to `2160`:
\[ 2160 = 360 \times 6 \]

### Step 3: Establish the multiplication pattern
The pattern we see is that each term is multiplied by an increasing integer:
- The first multiplication is by `3`
- The second multiplication is by `4`
- The third multiplication is by `5`
- The fourth multiplication is by `6`

### Step 4: Determine the missing term
To find the term before `6`, we need to multiply the previous term by `2`:
- Let the missing term be represented as `x`. Then:
\[ 6 = x \times 2 \]
Solving for `x` gives:
\[ x = \frac{6}{2} = 3 \]

### Conclusion
Thus, the missing term in the series is `3`.

### Final Answer
The number that should come in place of the question mark (?) is **3**.

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