A meeting hall has 20 seats in the first row, 24 seats in the second row, 28 seats in the third row, and so on and has in all 30 rows. How many seats are there in the meeting hall ?

8. A meeting hall has 20 seats in the first row, 24 seats in the second row, 28 seats in the third row, and so on and has in all 30 rows. How many seats are there in the meeting hall ?

Sol. The no. of seats in each row are as follows 20, 24, 28, .........

The no. of seats in each row form an A.P. with

First term (a) = 20

Difference between the no. of seats in two successive rows (d) = 4

Total no. of rows (n) = 30

Total no. of seats in 30 rows (S30) = ?

Sn = n/2[2a + (n – 1) d]

∴  S30 = 30/2 [2 (20) + (30 – 1) 4]

∴  S30 = 15 [40 + 116]

∴  S30 = 15 (156)

∴  S30 = 2340

∴ Total no. of seats in the meeting hall is 2340.