Question

In a 20 row theater, the number if 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 if seats in the theater.
b. find the total seating capacity of the theater.
c. front row tickets for a concert cost $60. After every 5 rows,the tickets price goes down by $5. What is the total amount of money generated by a full house?

Answer 1

@skullpatrol @ganeshie8 @Jack1

Answer 2

First row : 18
Second row : 18+3 = ?
Third row : 18+3+3 = ?
Fourth row : 18+3+3+3 = ?

Answer 3

so i keep added 3 but i dont get the rest:(

Answer 4

easy yes :)

Answer 5

so for part a, total number of seats in the theater is below sum :

18 + 21 + 24 + 27 + ...

Answer 6

^thats the series.
we're done with part a

Answer 7

thanks what b and c

Answer 8

for part b, u need to actually add all the seats to get the total number of seats

Answer 9

remember the partial sum formula for arithmetic series ?

Answer 10

the 18+3? im lost sorry

Answer 11

Sum of first "n" terms :

\(\large S_n = \dfrac{n}{2}\left[ 2a_1 + (n-1)d\right]\)

Answer 12

is n 18?

Answer 13

since there are 20 rows, \(n = 20\)
first row has 18 seats, so \(a_1 = 18\)
each row is incremented by 3, so \(d = 3\)

Answer 14

plug the values in formula and simplify

Answer 15

s= 20/2[2*18 1+(20-1)3]
s= 10[36 1+(19) 3]

Answer 16

s=10[36 (19) 3]

Answer 17

Yes :)

\(\large S_n = \dfrac{n}{2}\left[ 2a_1 + (n-1)d\right]\)


\(\large S_{20} = \dfrac{20}{2}\left[ 2*18 + (20-1)*3\right]\)

\(\large ~~~~~= 10\left[ 36 + (19)*3\right]\)

Answer 18

^^simplify

Answer 19

10(36+19 times 3) ?

Answer 20

=930

Answer 21

Perfect !
so, the total seating capacity of theater is \(930\)

Answer 22

thanks so what about c

Answer 23

for part C, u need to use the same formula FOUR times

Answer 24

c. front row tickets for a concert cost $60. After every 5 rows,the tickets price goes down by $5. What is the total amount of money generated by a full house?

Answer 25

Since there are 20 rows in the theater,
Cost of sitting in First 5 rows(1st row to 5th row) = 60
Cost of sitting in next 5 rows(6th row to 10th row) = 55
Cost of sitting in next 5 rows(11th row to 15th row) = 50
Cost of sitting in next 5 rows(15th row to 20th row) = 45

Answer 26

5th 60
10th 55
15 50
20 45

Answer 27

Exactly !
To get the money generated in First 5 rows :
tyou need to find out how many total seats are there in first 5 rows,
and multiply it by 60

Answer 28

use the same formula,
just replace \(n\) by \(5\)

Answer 29

\(\large S_n = \dfrac{n}{2}\left[ 2a_1 + (n-1)d\right] \)


\(\large S_5 = ? \)

Answer 30

s5= 5/2 [2*18+(5-1)3}
s5=2.5(26+4 times 3)

Answer 31

simplify all the way

Answer 32

and there is a mistake in ur second step : 2*18 = 36, NOT 26 okay ?

Answer 33

750/20=37.5

Answer 34

No wait, from where u getting these numbers lol

Answer 35

2.5 (120)
15 seats

Answer 36

\(\large S_n = \dfrac{n}{2}\left[ 2a_1 + (n-1)d\right] \)


\(\large S_5 = \dfrac{5}{2}\left[ 2*18 + (5-1)*3\right] \)

\(\large ~~~= \dfrac{5}{2}\left[ 36+ 12\right] \)

\(\large ~~~= \dfrac{5}{2}\left[ 48\right] \)

\(\large ~~~= 5\left[ 24\right] \)

\(\large ~~~= 120 \)

Answer 37

^^ So, there are aotal of t\(120\) seats in the first 5 rows.

Answer 38

Multiply it by 60 to get the money earned

Answer 39

so 6 seats per row?

Answer 40

so 360

Answer 41

Nope. there are a total of \(120\) seats in the first 5 rows.
and each seat earns 60.


So total money earned on first 5 rows = \(120 \times 60 = ?\)

Answer 42

7200?

Answer 43

Yep !

Answer 44

`120 sears` in the first 5 rows earn a money of `7200`

Answer 45

*120 seats

Answer 46

Okay ?
similarly u need to calculate how many seats are there in next 5 rows
and multiply it by 55

Answer 47

thanks so much that it thanks again

Answer 48

lol i though were done haha

Answer 49

np :) but the part c is not over yet...

there are 15 more rows in the back lol

Answer 50

u dont want more money ha ?

Answer 51

u just calculated the earning on first 5 rows.

Answer 52

lol im tried

Answer 53

15 more rows are yet to be calculated lol

Answer 54

haha yea ;)

Answer 55

Number of seats in next 5 rows (6th row to 10th row) :

http://www.wolframalpha.com/input/?i=10%2F2%282*18%2B%2810-1%29*3%29+-+120

Answer 56

multiply it by 55

Answer 57

195 times 55 =10725

Answer 58

Wow ! thats lots of money !!

Answer 59

Add it to ur previous amount

Answer 60

your first 5 rows earned `7200` ?

Answer 61

So total money earned from 1st row to 10th row = `7200+10725` = ?

Answer 62

lol someone is getting rich haha

Answer 63

Party !!!!

Answer 64

17925
lol why not party all day long haha

Answer 65

:)

lets get greedy... see how much next 5 rows earn u :

total number of seats in next 5 rows (11th row to 15th row) :
http://www.wolframalpha.com/input/?i=15%2F2%282*18%2B%2815-1%29*3%29+-+%28120%2B195%29

Answer 66

multiply it by 50

Answer 67

lol but i want to get a audi first haha

Answer 68

13500

Answer 69

hahah sure why not ;)

Answer 70

what about u what kind of car u want

Answer 71

yes add that to ur previous money : `7200+10725 + 13500`

Answer 72

^^thats the money earned by ur first 15 rows

Answer 73

31425

Answer 74

yes !

this is the number of seats in last 5 rows :
http://www.wolframalpha.com/input/?i=20%2F2%282*18%2B%2820-1%29*3%29+-+%28120%2B195%2B270%29

Answer 75

Multiply it by 45 and Enjoy.... !!

Answer 76

15525

Answer 77

46950 is the final answer

Answer 78

\(\large \color{red}{\checkmark}\)

Answer 79

here is ur gift for getting the correct answer everytime
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Answer 80

gtg... cya :)

Answer 81

thank you so much thanks for helping me understand this problem

Answer 82

thanks i love that car its perfect