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

Correct option is A

Solution

We are tasked to find the missing term in the series: 3, 8, 27, 112, (?), 3396 .

Step-by-Step Solution:

1. Observe the Series:

The terms are 3, 8, 27, 112, ?, 3396 .

Let's assume each term is derived using the previous term with a pattern of multiplication and addition.

2. Calculate the Ratios:

- From 3 to 8 :

3 \times 2 + 2 = 8

- From 8 to 27 :

8 \times 3 + 3 = 27

- From 27 to 112 :

27 \times 4 + 4 = 112

The pattern appears to be:

$$\text{Next term} = \text{Current term} \times n + n$$​

Where n = 2, 3, 4, $$\dots .$$​

3. Find the Missing Term:

For 112 to the next term, n = 5 :

$$112 \times 5$$​+ 5 = 560 + 5 = 565

4. Verify for the Last Term:

For 565 to 3396 , n = 6 :

$$565 \times 6$$​ + 6 = 3390 + 6 = 3396

Final Answer:

$$\boxed{565}$$​