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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
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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freckles
 one year ago
Best ResponseYou've already chosen the best response.1hmmm 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So what answer would it be using that?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.21 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,

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so in general to find the (n+1)th term from the nth you do: \[\frac{n(n+1)(2n+1)}{6}+(n+1)^2\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1where n(n+1)(2n+1)/6 was the nth term

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and (n+1)^2 was what you needed to add to get the next number (that I called (n+1)th

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so mathstudent is right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I don't think he ever wrong :p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0he was right, thank you guys
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