Respuesta :
Step-by-step explanation:
Given:
Theater has 15 seats
Last Row has 72 seats.
Theater has a total of 870 seats.
Unknown: Number of rows
Number of seats in each row.
Equations: Since we know the total number of seats the Theater has we can use the sum of arithmetic series
[tex]s = \frac{a _{1} + a _{n} }{2} n[/tex]
Where a1 is the first row of seats
s is total number of seats
an is last row of seats
n is number of rows.
[tex]870 = \frac{15 + 72}{2} (n)[/tex]
[tex]870 = \frac{87}{2} n[/tex]
[tex]2(870) = 87n[/tex]
[tex]20 = n[/tex]
So we have 20 rows.
To find how many seats does each row increase, we use this formula,
[tex]a _{n} = a + (n - 1)d[/tex]
Let use the 20th row as an example,
[tex]a _{20} = 15 + (19)d[/tex]
[tex]72 = 15 + (19)d[/tex]
[tex]57 = 19d[/tex]
[tex]3 = d[/tex]
So the common difference is 3.
So the seats of each row increase by 3.
