Question

There are 30 rows of seats in a large arena. The first row contains 10 seats. Each successive row increases by 3 seats. How many seats are in the last row? How many seats are there in all ?

Answer 1

Total number of seats in arena [Sn] = 1,605 seats

Explanation:

Given:

Total number of rows (n) = 30

Number of seats in first row (a) = 10

Number of extra seats in per row (d) = 3 more than first row

Find:

Total number of seats in arena (Sn)

Computation:

This is Arithmetic progression problem.

So,

Total number of seats in arena [Sn] = [n/2][2a + (n-1)d]

Total number of seats in arena [Sn] = [30/2][2(10) + (30-1)(3)]

Total number of seats in arena [Sn] = [15][20 + (29)(3)]

Total number of seats in arena [Sn] = [15][20 + 87]

Total number of seats in arena [Sn] = [15][107]

Total number of seats in arena [Sn] = 1,605 seats