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anonymous

  • one year ago

The 99th pyramidal number is 328,350. That would make quite a stack of basketballs! What number must you add to 328,350 to get the 100th pyramidal number? A. 1000 B. 55 C. 100 D. 10,000 E. 328,350

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  1. mathstudent55
    • one year ago
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    D

  2. freckles
    • one year ago
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    hmmm pyramid numbers... well the first few pyramid numbers are: 1,5,14,30,55,91,140,.... And the n term can be given by : \[\sum_{k=1}^{n} k^2=\frac{n(n+1)(2n+1)}{6}\] so you have the 99th term which is given by: \[\sum_{k=1}^{99} k^2=\frac{99(99+1)(2(99)+1)}{6}\] anyways let me give you an example of what is going on here: say we have the 3rd term which is given by: \[\sum_{k=1}^{3} k^2=\frac{3(3+1)(2(3)+1)}{6}\] which is 3(4)(7)/6=12(7)/6=2(7)=14 and we wanted to know what to add to 14 to get the next term well notice we are adding squared numbers in that series above so 14+4^2 to get the 4th term from the 3rd term

  3. anonymous
    • one year ago
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    So what answer would it be using that?

  4. mathstudent55
    • one year ago
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    1 1 + 4 = 5 5 + 9 = 14 14 + 16 = 30 30 + 25 = 55 Notice that to find the 2nd pyramidal number, you add 4 = 2^2 to the first one. That means to find the 100th pyramidal number, you add 100^2 to the 99th number,

  5. freckles
    • one year ago
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    so in general to find the (n+1)th term from the nth you do: \[\frac{n(n+1)(2n+1)}{6}+(n+1)^2\]

  6. freckles
    • one year ago
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    where n(n+1)(2n+1)/6 was the nth term

  7. freckles
    • one year ago
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    and (n+1)^2 was what you needed to add to get the next number (that I called (n+1)th

  8. anonymous
    • one year ago
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    so mathstudent is right?

  9. freckles
    • one year ago
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    yes (99+1)^2

  10. freckles
    • one year ago
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    I don't think he ever wrong :p

  11. anonymous
    • one year ago
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    he was right, thank you guys

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