A group of 540 persons is to be seated row wise such that the number of persons in each row is 4 less than in the previous row. Which of the following number of rows is not possible? 

Explanation:Sn=n2×[2a+(n−1)d]

Given that 540 people are to be seated in rows such that each row contains 4 fewer people than the

previous row. We need to find which of the given numbers of rows is not possible.

Let  = number of rows and  = the number of people seated

The number of people in the second row is  in the third row is  and so on.

The total number of people seated is 

This is an arithmetic series with first term  , common difference d = -4 and number of terms n .

The sum of an arithmetic series is given by ​​​​​​

⇒ 

⇒ 

Checking Option 1: n = 5

⇒ 
 

⇒ x = 116

This is possible, so 5 rows is possible.

Checking Option 2: n = 6

⇒ 
⇒ 

This is possible, so 6 rows is possible.

Checking Option 3: n = 8

⇒ 

⇒  , which is not an integer, 8 rows is not possible.

Checking Option 4: n = 9

​​

⇒ 

⇒ 

This is possible, so 9 rows is possible.

The number of rows that is not possible is Option 3).