A drivein theater has spaces for 20 cars in the first parkin

A drive-in theater has spaces for 20 cars in the first parking row, 22 in the second, 24 in third, and so on. A there are 21 rows in the theater, find the number of cars that can be parked.

Solution

So , cars in row : 20, 22 , 24, ........

It forms an Arithmetic Progression(A.P) with a = 20 and d= 2

21 rows are there , i.e n=21

Sum of n terms of A.P , S_n = n/2[2a + (n-1)d ]

No.of cars that can be parked = sum of cars in 21 rows

= S₂₁ = 21/2[2(20) + (21-1)2] = 21/2 X 80 = 840

No.of cars parked = 840