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anonymous
 one year ago
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?
anonymous
 one year ago
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?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the formula for that is sum = (n/2)[2a+(n1)d] where n=24 d= 4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@nincompoop @TheSmartOne

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just substitute the values and youll get the answer

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2This 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
 one year ago
Best ResponseYou've already chosen the best response.0ow my mistake n= 24 d= 5 a= 4 a is the first row

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok:) So I'll just plug in to solve. Can u check when im done?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0an=4+5(241) an=4+5(23) an=119??

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Row 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
 one year ago
Best ResponseYou've already chosen the best response.0ok:) How do we do that?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(\Large S_n = \dfrac{n(a_1 + a_n)}{2}\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2n = 24 a1 = 4 a24 = 119

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(\Large S_{24} = \dfrac{24(4 + 119)}{2}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.2dw:1439514122421:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2We 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
 one year ago
Best ResponseYou've already chosen the best response.2\(\Large a_1= 30\) 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
 one year ago
Best ResponseYou've already chosen the best response.2You are correct.
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