Word problem

Question

In a 20 row theatre, the number of each seats increases by 3 with each successive row. The first row has 18 seats.

a. write an arithmetic series in summation notation to represent the number of seats in the theatre.

b. what is the total seating capacity of the theatre?

c. front row seats cost 60 dollars. After every 5 rows, the price drops 5 dollars. What is the amount generated by a full house?

Answer 1

First number,a1 = 18

Common difference, d = 3

a)

an=a1+(n-1)d

    =18+(n-1)3

   =3n+15

   20

= ∑     3n+15

  n =1

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b) 

Sn  = ∑ 3n+15

        =3∑n+15∑1

       =3 n(n+1)/2+15n

Sn =3* 20(20+1)/2+15(20)

   =30(21)+300

   =630+300

    =930

Total number of seats 930

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c)

Write a series for the number of seats in each set of 5 rows.

   5                     10                      15                     20

= ∑     3n+15  ;   ∑     3n+15     ;    ∑     3n+15 ;    ∑ 3n+15

  n =1                n =6                     n = 11            16

=120;195;270;345

The ticket prices for each set of 5 rows.

$60;$55;$50;$45

=120*60+195*55+270*50+345*45

=$46950