What will come in place of the question mark in the series
3 8 27 112 ? 3396

Options

A. 565
B. 452
C. 560
D. 678

Answer

To find the missing number in the series 3, 8, 27, 112, ?, 3396, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
Let's look at the first few terms of the series:
- The first term is 3.
- The second term is 8.
- The third term is 27.
- The fourth term is 112.

We will try to find a relationship between these numbers.

### Step 2: Analyze the relationship
1. From 3 to 8:
- Multiply 3 by 2 and add 2:
\[ 3 \times 2 + 2 = 6 + 2 = 8 \]

2. From 8 to 27:
- Multiply 8 by 3 and add 3:
\[ 8 \times 3 + 3 = 24 + 3 = 27 \]

3. From 27 to 112:
- Multiply 27 by 4 and add 4:
\[ 27 \times 4 + 4 = 108 + 4 = 112 \]

### Step 3: Continue the pattern
Now, we will apply the same logic to find the next term:
- From 112 to the question mark:
- Multiply 112 by 5 and add 5:
\[ 112 \times 5 + 5 = 560 + 5 = 565 \]

### Step 4: Verify the next term
Now, we will check if this pattern holds for the next term:
- From 565 to 3396:
- Multiply 565 by 6 and add 6:
\[ 565 \times 6 + 6 = 3390 + 6 = 3396 \]

### Conclusion
The missing term in the series is **565**.