anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I got 930
radar
  • radar
Yess I messed up
anonymous
  • anonymous
for each of the end sections \[\sum_{i=4}^{23}i\] for te middle section \[\sum_{i=10}^{29}i\]

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anonymous
  • anonymous
do you know the general form of the sum of an arithmetic sequence nicolenova
anonymous
  • anonymous
yeah
anonymous
  • anonymous
ok then you just need to compute those sums, multiply the end one by two to account for both sections and add them up.
anonymous
  • anonymous
do you see where the sums come from?
anonymous
  • anonymous
i don't really get the formulas
anonymous
  • anonymous
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 \[\sum_{i=10}^{29}i\]
anonymous
  • anonymous
the end sections are the same except starting with 4 in the first row and going to 23 in the 20th row.
anonymous
  • anonymous
wait there isn't 10 rows, there's 20, and the first has 10 seats
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
i dont think that is right ms bio. Just adding the first 8 rows of the middle section you have more than 75
anonymous
  • anonymous
10+11+12+13+14+15+16+17>75
anonymous
  • anonymous
yeah, Actually 75 is only the total seat in the 20th row.. hang on I think i'm getting it right now...heheheh
anonymous
  • anonymous
k let me know if you get the same answer as me, I have 930 total seats
anonymous
  • anonymous
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
anonymous
  • anonymous
I just solved the last row first...heheheh LOL
anonymous
  • anonymous
good I'm glad it came out the same
anonymous
  • anonymous
Yeah, that is one of the reasons I resorted to become a Bio major...I get so reckless in solving...heheheh

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