Question

A school auditorium has to be constructed with a capacity of 2000 people. The chairs in the auditorium are arranged in a concave shape facing towards the stage in such a way that each succeeding row has 5 seats more than the previous one.

(i) If the first row has 15 seats, then how many seats will be there in 12th row?

(ii) If there are 15 rows in the auditorium, then how many seats will be there in the middle row?  

(iii) If total 1875 guests were there in the auditorium for a particular event, then how many rows will be needed to make all of them sit?

OR

If total 1250 guests were there in the auditorium for a particular event, then how many rows will be left blank out of total 30 rows?

Answer 1

(i) a = 15, d = 5

a₁₂ = 15 + 11 × 5 = 70

(ii) n = 15

Middle row = 8^th row

a₈ = 15 + 7 × 5 = 50

(iii) 1875 =n/2 [2 × 15 + (n − 1) × 5]

⟹ n² + 5n − 750 = 0

(n + 30) (n − 25) = 0 

⟹ n = 25

∴ Total number of rows required = 25

OR

1250 =n/2 [2 × 15 + (n − 1) × 5]

⟹ n² + 5n − 500 = 0

(n + 25) (n − 20) = 0 

⟹ n = 20

∴ Number of rows left = 30 − 20 = 10