What will come in place of the '?' in the given series.
3, 4, 9, 28, 113, ?

Options

A. 540
B. 566
C. 587
D. 592

Explanation

To find the missing number in the series: 3, 4, 9, 28, 113, ?, we will analyze the pattern in the sequence step by step.

### Step 1: Identify the pattern
Let's look at the differences and operations between consecutive terms in the series.

- From 3 to 4:
\[ 3 \times 1 + 1 = 4 \]

- From 4 to 9:
\[ 4 \times 2 + 1 = 9 \]

- From 9 to 28:
\[ 9 \times 3 + 1 = 28 \]

- From 28 to 113:
\[ 28 \times 4 + 1 = 113 \]

### Step 2: Continue the pattern
Now we need to find the next term after 113. Following the identified pattern, we multiply by 5 and then add 1.

- From 113 to the next term:
\[ 113 \times 5 + 1 \]

### Step 3: Calculate the next term
Now we perform the calculation:
\[ 113 \times 5 = 565 \]
Adding 1:
\[ 565 + 1 = 566 \]

### Conclusion
Thus, the missing number in the series is:
\[ \boxed{566} \]