What should come in place of the question mark(?) in the following number series?
3 5 15 ? 1125 84375

Options

A. 75
B. 20
C. 45
D. 80

Answer

To find the missing number in the series 3, 5, 15, ?, 1125, 84375, we need to identify the pattern in the series.

### Step 1: Identify the relationship between the numbers
Let's analyze the given numbers:
- The first number is 3.
- The second number is 5.
- The third number is 15.

### Step 2: Determine the multiplication pattern
We can see that:
- \(3 \times 5 = 15\)

Now, let's see if there is a consistent multiplication factor for the next number in the series.

### Step 3: Find the next number
If we assume that the next number (the one represented by the question mark) is \(x\), we can try to find \(x\) using the multiplication pattern:
- \(15 \times x = 1125\)

### Step 4: Solve for \(x\)
To find \(x\), we can rearrange the equation:
\[ x = \frac{1125}{15} \]
Calculating this gives:
\[ x = 75 \]

### Step 5: Verify the pattern with the next number
Now, let's check if this pattern holds for the next number:
- \(75 \times 15 = 1125\)
- \(1125 \times 75 = 84375\)

Both calculations confirm that our assumption is correct.

### Conclusion
The missing number in the series is **75**.