Question

In a 20-row theatre, the number of seats in a row increases by three with each successive row. The first row has 18 seats.
a. write an arithmetic series to represent the number of seats in a theatre
b. find the total seating capacity of the theater.
c. front row tickets for a concert cost 60$. after every 5 rows, the ticket price goes down by 5$. what is the total amount of money generated by a full house?
(show work please)

Answer 1

Well, to start you off, I think the arithmetic sequence formula is:
f(n)=f(n-1)+3
n>1
I'm not too sure, which is my sole reason of not continuing the assistance.

Answer 2

Arithmetic Series (\(S_n\)) means the sum (S) of a certain number of terms (n).
In your problem, you are looking for (\(S_{20}\))

I attached the formula, where \(a_1\) is the first term, which in your problem is 18
and \(a_n\) is the number of chairs in row 20.

First you have to do is to find \(a_{20}\) using \(a_n=a_1+(n-1)d\) (where d is the difference, which is 3 in your problem) .. substitute the given values in the formulas that i gave you. That is for letter question a.

Answer 3

would it look like this?

Answer 4

@Data_LG2

Answer 5

except i think 20 is on the top instead of k

Answer 6

i think it should be \[\sum_{n=1}^{20}n+3\] ?? but again i'm still confused

Answer 7

the answer book says this

Answer 8

oh i think i understand now..

so

If we will work backwards,