Question

A 20-row theater has three sections of seating. In each section,
the number of seats in a row increases by one with each successive row.The
first row of the middle section has 10 seats.The first row of each of the two side
sections has 4 seats.
a. Find the total number of chairs in each section.Then find the total seating
capacity of the theater.
b. Write an arithmetic series to represent each section.

Answer 1

I got 930

Answer 2

Yess I messed up

Answer 3

for each of the end sections

\[\sum_{i=4}^{23}i\]

for te middle section

\[\sum_{i=10}^{29}i\]

Answer 4

do you know the general form of the sum of an arithmetic sequence nicolenova

Answer 5

yeah

Answer 6

ok then you just need to compute those sums, multiply the end one by two to account for both sections and add them up.

Answer 7

do you see where the sums come from?

Answer 8

i don't really get the formulas

Answer 9

ok we'll do the middle one. There are 10 rows to start, then the next has 11, then 12,...

so the total seating is 10+11+12+13+... and we go until we have 20 terms. The 20th term will be 10+19=29 so we have

\[\sum_{i=10}^{29}i\]

Answer 10

the end sections are the same except starting with 4 in the first row and going to 23 in the 20th row.

Answer 11

wait there isn't 10 rows, there's 20, and the first has 10 seats

Answer 12

yeah there are 20 rows and 10 seats in the first. so we have 10 seats in the first row, 11 seats in the second row, 12 in the third,..., 29 in the 20th row. And we add all the seats together

Answer 13

I hope i'm getting this right:

15+3n
15+3(20)
=15+60
=75

I think its a small theater lol! it only has 75 seating capacity

Answer 14

i dont think that is right ms bio. Just adding the first 8 rows of the middle section you have more than 75

Answer 15

10+11+12+13+14+15+16+17>75

Answer 16

yeah, Actually 75 is only the total seat in the 20th row.. hang on I think i'm getting it right now...heheheh

Answer 17

k let me know if you get the same answer as me, I have 930 total seats

Answer 18

yeah, the same! I used the arithmetic sequence:
s=n/2 (2*first term+(n-1)d)
n=20
first term is 18
d is 3
then you'll get 930

Answer 19

I just solved the last row first...heheheh LOL

Answer 20

good I'm glad it came out the same

Answer 21

Yeah, that is one of the reasons I resorted to become a Bio major...I get so reckless in solving...heheheh