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taylorx
 2 years ago
ALGEBRA 2 HELP PLEASE WILL FAN AND MEDAL.
In a 20row 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)
taylorx
 2 years ago
ALGEBRA 2 HELP PLEASE WILL FAN AND MEDAL. In a 20row 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)

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tafkas77
 2 years ago
Best ResponseYou've already chosen the best response.2Do you understand this topic at all, or are you completely lost?

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0@tafkas77 i'm completely lost. :(

tafkas77
 2 years ago
Best ResponseYou've already chosen the best response.2That's perfectly fine. :) Just so you know, you don't have to fan me. I don't mind helping when I can. :) Give me just a moment, okay?

tafkas77
 2 years ago
Best ResponseYou've already chosen the best response.2I would love to stay and help you, but something has just come to my attention. Here is an example that I worked out for you, okay? Arithmetic sequences allow you to predict the next number in a sequence by defining the pattern. If that doesn't make sense, I can give an example in a random sequence: 2, 6, 14, Here's the equation for this sequence: a_n +1 = 2a_n + 2 a_2 = 2(2) + 2; which equals 6. That's the second term. a_3 = 2(6) + 2; which equals 14. That's the third term. As you can see, you ALWAYS add the number you got from the previous equation to the next equation. This same thing can be applied to your question, okay? we know that a_n + 3 = the amount of seats in the room (or S) For the first row, we could look at it like this: a_n + 3 = 18 If you finish this equation you'll find that a_n = 15. :)

tafkas77
 2 years ago
Best ResponseYou've already chosen the best response.2If you continue on with this equation, you can find out the next row, and the next row, and the next row.... :D Hope that helped!

tafkas77
 2 years ago
Best ResponseYou've already chosen the best response.2Okay. Where were you lost? Or  from 1  10, 1 being completely lost and 10 being confident, how do you feel about this question?

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.01 @tafkas77 . can you just help me through each step>? that'd be great

tafkas77
 2 years ago
Best ResponseYou've already chosen the best response.2I'm not sure how best to help you. Would you please give me a moment?

tafkas77
 2 years ago
Best ResponseYou've already chosen the best response.2I don't think I am equipped to help you on this one. I'm sorry. :/ @amistre64

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3wow, taylor and tafkas look soooo much alike its hard to tell which post is which :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3In a 20row theatre, there are going to be rows 1 thru 20 the number of seats in a row increases by three with each successive row. each new row has 3 more seat than the one before it The first row has 18 seats. we know the first row has 18 seats row 1 has 18 seats row 2 has: 18+3 seats row 3 has: 18+3 + 3 seats row 4 has: 18+3 +3 +3 seats, this can start to be written as row 1 has 18 + 3(0) seats row 2 has: 18 + 3(1) seats row 3 has: 18 + 3(2) seats row 4 has: 18 + 3(4) seats does this make sense to you?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3row 4 has: 18 + 3(3) seats ... typoed it

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3row 1 has 18 + 3(0) seats row 2 has: 18 + 3(1) seats row 3 has: 18 + 3(2) seats row 4 has: 18 + 3(3) seats ^^ ^^^ this value compares to this value notice that the nth row has 3(n1) seats, therefore \[R_n=18+3(n1)~seats\]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3when we know what produces the sequence of seats per row, we can then create a series, which is just a summation of the sequence:\[\sum_{n=1}^{k}18+3(n1)\] or simplified to \[\sum_{n=1}^{k}15+3n\]

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0so would rn=18+3(n1) seats be the arithemetic series @amistre64

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3no, the vocabulary for this type of stuff is: a sequence represents a recurrsive pattern: 18, 21, 24, 27, 30, ... this pattern can be generated by the recurrsive equation: 15+3n, for simplicities sake a series is the sum of a sequence: 18 + 21 + 24 + 27 + 30 + ...

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3a series keeps a running tab, a cumulative account of what has happened

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0so how do you write the arithmetic series ? @amistre64

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3its just the sum of the recursive equation:\[\sum_{n=1}^{20}15+3n\]

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0@amistre64 thank you. so how do you find the seating capacity, thank you.

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3the total number of seats can be worked out by hand, or by mathing techniques

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3notice that the summation proceeds as: row1 + row 2 + row 3 + row 4 ... +row 20  total number of seats

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3row1: 15+3(1) row2: 15+3(2) row3: 15+3(3) row4: 15+3(4) .... row20: 15+3(20)  15(20) + 3(1+2+3+4+...+20)

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0@amistre64 thank you so much! now all i need is : 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?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3so, this tells us that we simply need to take the sum of the first 5 rows, and times it by 60 add that to the sum of the last 15 rows, times it by 5

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3\[65\sum_{1}^{5}(15+3n)+5\sum_{6}^{20}(15+3n)\] \[65(15)(5)(3)\sum_{1}^{5}n+5(15)(15)(3)\sum_{6}^{20}n\]

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0@amistre64 is there anyway to simplify that.

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0and @amistre64 what is the total money generated by a full house?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3not really, but its not that bad if you work it out in steps

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3how many seats are in the first 5 rows? times 65 plus, how many seats are in the last 15 rows? times that by 5 add up the results

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0okay thank you very much:) @amistre64

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3try it out, and if you need me to dbl chk your results, i can do that :) i just want to steer clear of just handing over an answer is all

tafkas77
 2 years ago
Best ResponseYou've already chosen the best response.2@amistre64 I love your methods. Lifesaver! :D Thank you so much! You helped both of us! :)

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0@amistre64 for the recursive equation that you gave me on step a, is it supposed to be written with "k" on top or "20" on top , because you wrote it as both. thanks

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.320 is more suited to the problem, im just forgot to make the general case 100% suited to your situation :) but good call on that

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0@amistre64 thanks :) you are such a lifesaver

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3:) might have to bail out soon, my kids are causing issues at school :/

taylorx
 2 years ago
Best ResponseYou've already chosen the best response.0@amistre64 sorry to hear that, come back soon :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3ill be back tomorrow ;) good luck
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