Question 1017771
<pre>

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&#8729;4, 4&#8729;5, 5&#8729;6, 6&#8729;7, 7&#8729;8, 8&#8729;9

So the sequence is:

1&#8729;3&#8729;4, 2&#8729;4&#8729;5, 3&#8729;5&#8729;6, 4&#8729;6&#8729;7, 5&#8729;7&#8729;8, 6&#8729;8&#8729;9

So it is:

a<sub>n</sub> = n(n+2)(n+3)

a<sub>1</sub> = 1(1+2)(1+3) = 1(3)(4) = 12
a<sub>2</sub> = 2(2+2)(2+3) = 2(4)(5) = 40
a<sub>3</sub> = 3(3+2)(3+3) = 3(5)(6) = 90
a<sub>4</sub> = 4(4+2)(4+3) = 4(6)(7) = 168
a<sub>5</sub> = 5(5+2)(5+3) = 5(7)(8) = 280
a<sub>6</sub> = 6(6+2)(6+3) = 6(8)(9) = 432

Edwin</pre>