Question

An amphitheatre has 19 seats in the first row, 22 in the second, 25 in the third, and so on, for 29 rows. How many seats are in the amphitheatre?

The amphitheatre has
seats.
PLEASE HELP

Answer 1

The total number of seats in the amphitheater is 1769

Explanation:

The number of seats in the first row = 19

The number of seats in second row = 22

The number of seats in third row = 25

The total number of rows = 29

The question can be written as

19, 22, 25, ....

The expression is an arithmetic progression

where a1 = 19, d = 22 - 19 = 3, n = 29

By formula,

`a_(n) = a_(1) + (n - 1) d`

Substituting the values in the equation, we get

= 19 + (29 - 1) 3

= 19 + (28 * 3)

the last row seats, l = 103

The total number of seats,
`S_(n) = n /2 [ a + l]`

`S_(n) = 29 / 2 [ 19 + 103]`

= 1769