Question

There is an auditorium with 27 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 how many total seats are there in the auditorium?

Answer 1

The number of seats arranged row-wise is as follows: 20, 22, 24 ..............

This sequence is in A.P.

∴ a = 20, d = 22 – 20 = 2, n = 27

Now, S_n = `"n"/2 [2"a" + ("n" - 1)"d"]`  ......[Formula]

S₂₇ = `27/2 [2 xx 20 + (27 - 1) xx 2]`

= `27/2 [40 + 26 xx 2]`

= `27/2 [40 + 52]`

= `27/2 xx 92`

= 27 × 46

∴ S₂₇ = 1242

∴  The total seats in auditorium are 1242.