An auditorium has 70 rows of seats The first row contains 60

An auditorium has 70 rows of seats. The first row contains 60 seats. As you move to the rear of the auditorium, each row had 4 more seats than the previous row.

How many seats are in the auditorium?

Solution

The number of seats increment would be,

60,64,68,..........70 terms

T_n = a + (n-1)d = T₇₀ = 60 + (70-1)4 = 336

Total number of seats in the auditorium = Sum till n terms = (n/2)(2a + (n-1)d) = (70/2)(2x60 + (70-1)4) = 13860

Total number of seats = 13860