Question

A hall has 35 rows. Each successive row contains two additional seat. If the first row has 20 seats, how many seats are in the hall?

Answer 1

There are 1,890 seats in the hall

Explanation:

The number of seats in the first row = 20 seats

The number of rows in the hall = 35 rows

The number of additional seat per row = 2 Seat

Therefore, the sequence of seats in the hall is an arithmetic sequence with the first term, a = 25, the common difference, d = 2, and the number of terms, n = 35

The formula for finding the sum of n-terms of an arithmetic progression, Sₙ is given as follows;

Sₙ = n/2 × [2·a + (n - 1)·d]

Plugging in the values, we get;

Sₙ = 35/2 × [2 × 25 + (35 - 1)×2] = 1890 seats

Therefore, there are 1,890 seats in the hall.