anonymous
  • anonymous
The seats at a local baseball stadium are arranged so that each row has five more seats than the row in front of it. If there are four seats in the first row, how many total seats are in the first 24 rows?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
the formula for that is sum = (n/2)[2a+(n-1)d] where n=24 d= 4
anonymous
  • anonymous
anonymous
  • anonymous
just substitute the values and youll get the answer

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mathstudent55
  • mathstudent55
This can be written as a geometric sequence where d, the common difference is 5. row 1: 4 = 4 + (5 * 0) = 4 = a1 row 2: 4 + 5 = 4 + (5 * 1) = 9 = a2 row 3: 9 + 5 = 4 + (5 * 2) = 14 = a3 row 4: 14 + 5 = 4 + (5 * 3) = 19 = a3 ... row n: an = a1 + d(n - 1) \(\Large a_n = a_1 + d(n - 1)\) With this formula, you can find the number of seats on the 24th row. Then the sum of the first n terms of an arithmetic series is: \(\Large S_n = \dfrac{n(a_1 + a_n)}{2} \)
anonymous
  • anonymous
ow my mistake n= 24 d= 5 a= 4 a is the first row
anonymous
  • anonymous
Ok:) So I'll just plug in to solve. Can u check when im done?
anonymous
  • anonymous
yeah sure
anonymous
  • anonymous
an=4+5(24-1) an=4+5(23) an=119??
mathstudent55
  • mathstudent55
Row 24: \(\Large a_n = a_1 + d(n - 1)\) \(\Large a_{24} = 4 + 5(24 - 1)\) \(\Large a_{24} = 119\) Row 24 alone has 119 seats. Now we need to use the Sn formula to sum all the rows.
anonymous
  • anonymous
ok:) How do we do that?
mathstudent55
  • mathstudent55
\(\Large S_n = \dfrac{n(a_1 + a_n)}{2}\)
mathstudent55
  • mathstudent55
n = 24 a1 = 4 a24 = 119
mathstudent55
  • mathstudent55
\(\Large S_{24} = \dfrac{24(4 + 119)}{2}\)
anonymous
  • anonymous
1476!
mathstudent55
  • mathstudent55
correct
anonymous
  • anonymous
Thanks :D
anonymous
  • anonymous
I have one more? This time, I have the answer for it lol Each trip, a bus drops off more fans at a concert. On the first trip, the bus dropped off 30. On the 14th trip, which was the last one, the bus dropped off 95 fans. How many fans did the bus deliver to the concert in total? Answer:875?
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
We need to assume the bus always drops off the same number of extra fans each time. If this assumption is correct, we have an arithmetic sequence.
mathstudent55
  • mathstudent55
\(\Large a_1= 30\) and \(\Large a_{14} = 95\) Since we already have the first and last term of the sequence, we can use the sum formula. \(\Large S_n = \dfrac{n(a_1 + a_n)}{2}\) \(\Large S_{14} = \dfrac{14(30 + 95)}{2} = 875\)
mathstudent55
  • mathstudent55
You are correct.
anonymous
  • anonymous
Thanks!!!
mathstudent55
  • mathstudent55
You're welcome.

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