(i)
Since each row is increasing by 10 seats, so it is an AP with first term a = 30,
and common difference d = 10.
So number of seats in 10th row = α10 = a + 9d
= 30 + 9 x 10 = 120
(ii)
Sn = n2 ( 2a + (n-1)d)
1500 = n/2 ( 2 x 30 + (n-1)10)
3000 = 50n + 10n2
n2 + 5n - 300 = 0
n2 + 20n -15n – 300 = 0
(n+20) (n-15) = 0
Rejecting the negative value, n = 15
OR
No. of seats already put up to the 10th row = S10
S10 = 10/2 {2 x 30 + (10-1)10)}
= 5(60 + 90) = 750
So, the number of seats still required to be put are 1500 - 750 = 750
(iii)
If no. of rows = 17
then the middle row is the 9th row
α8 = a + 8d
= 30 + 80
= 110 seats