There is an auditorium with 35 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row, and so on. Find the number of seats in the twenty fifth row.

4. There is an auditorium with 35 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row, and so on. Find the number of seats in the twenty fifth row.

Sol. Since the no. of seats in each row of the  auditorium are 20, 22, 24, ......

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

No. of seats in first row (a) = 20

Difference in no. of seats in two successive rows is (d) = 2

No. of seats in 25th row = t25 = ?

tn = a + (n + 1) d

∴ t25 = a + (25 – 1) d

∴ t25 = 20 + 24 (2)

∴ t25 = 20 + 48

∴ t25 = 68

∴  There are 68 seats in 25th row.