SOLUTION: what is the rule for 12, 40, 90, 168, 280, 432

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Question 1017771: what is the rule for 12, 40, 90, 168, 280, 432
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

12, 40, 90, 168, 280, 432

I first tried dividing them by 

1, 2, 3, 4, 5, 6 

respectively and got

12, 20, 45, 42, 56, 72

Then I recognized that as the pattern:

3∙4, 4∙5, 5∙6, 6∙7, 7∙8, 8∙9

So the sequence is:

1∙3∙4, 2∙4∙5, 3∙5∙6, 4∙6∙7, 5∙7∙8, 6∙8∙9

So it is:

an = n(n+2)(n+3)

a1 = 1(1+2)(1+3) = 1(3)(4) = 12
a2 = 2(2+2)(2+3) = 2(4)(5) = 40
a3 = 3(3+2)(3+3) = 3(5)(6) = 90
a4 = 4(4+2)(4+3) = 4(6)(7) = 168
a5 = 5(5+2)(5+3) = 5(7)(8) = 280
a6 = 6(6+2)(6+3) = 6(8)(9) = 432

Edwin