Question

Algebra 2, help with 3 part problem!?

Architecture: In a 20-row theater, the number of seas in a row increase by three with each successive row. The first row has 18 seats:

a. Write an arithmetic series to represent the number of 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 ticket price goes down by $5. What is the total amount of One generated by a full house?!

Just part C

Answer 1

here a=18,c.d.=3,n=20

it is an A.P
\[tn=a+\left( n-1 \right)d\]
use the above formula and calculate t20
A.P. series is
18+21+24+27+..........
\[Sn=\frac{ n }{ 2 }\left\{ 2a+\left( n-1 \right)d \right\} \]
substitute the values of a,n & d &get the values of S20
or you can calculate \[Sn=\frac{ n }{ 2 }\left( a+l \right),where l=t20\]

Answer 2

\[cost=60\left( 18+21+24+27+30 \right)+65\left( 33+36+39+42
+45 \right+68\left( 48+51+54+57+60 \right)\]+71 and so on