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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?

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  1. anonymous
    • one year ago
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    the formula for that is sum = (n/2)[2a+(n-1)d] where n=24 d= 4

  2. anonymous
    • one year ago
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    @nincompoop @TheSmartOne

  3. anonymous
    • one year ago
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    just substitute the values and youll get the answer

  4. mathstudent55
    • one year ago
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    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: \(\Large S_n = \dfrac{n(a_1 + a_n)}{2} \)

  5. anonymous
    • one year ago
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    ow my mistake n= 24 d= 5 a= 4 a is the first row

  6. anonymous
    • one year ago
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    Ok:) So I'll just plug in to solve. Can u check when im done?

  7. anonymous
    • one year ago
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    yeah sure

  8. anonymous
    • one year ago
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    an=4+5(24-1) an=4+5(23) an=119??

  9. mathstudent55
    • one year ago
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    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.

  10. anonymous
    • one year ago
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    ok:) How do we do that?

  11. mathstudent55
    • one year ago
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    \(\Large S_n = \dfrac{n(a_1 + a_n)}{2}\)

  12. mathstudent55
    • one year ago
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    n = 24 a1 = 4 a24 = 119

  13. mathstudent55
    • one year ago
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    \(\Large S_{24} = \dfrac{24(4 + 119)}{2}\)

  14. anonymous
    • one year ago
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    1476!

  15. mathstudent55
    • one year ago
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    correct

  16. anonymous
    • one year ago
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    Thanks :D

  17. anonymous
    • one year ago
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    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?

  18. mathstudent55
    • one year ago
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    |dw:1439514122421:dw|

  19. mathstudent55
    • one year ago
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    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.

  20. mathstudent55
    • one year ago
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    \(\Large a_1= 30\) and \(\Large a_{14} = 95\) Since we already have the first and last term of the sequence, we can use the sum formula. \(\Large S_n = \dfrac{n(a_1 + a_n)}{2}\) \(\Large S_{14} = \dfrac{14(30 + 95)}{2} = 875\)

  21. mathstudent55
    • one year ago
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    You are correct.

  22. anonymous
    • one year ago
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    Thanks!!!

  23. mathstudent55
    • one year ago
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    You're welcome.

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