Question 1099554
<pre><font size = 5><b>
{a<sub>n</sub>}: -1, 3, -6, 10, -15, 21 ....?

Double them and get

{2a<sub>n</sub>}: -2, 6, -12, 20, -30, 42 ....

Write them as the product of two integers:

{2a<sub>n</sub>}: -1×2, 2×3, -3×4, 4×5, -5×6, 6×7 ....

To get the alternating signs we use the factor (-1)<sup>n</sup>×

{2a<sub>n</sub>}: (-1)<sup>1</sup>×1×2, (-1)<sup>2</sup>×2×3, (-1)<sup>3</sup>×3×4, (-1)<sup>4</sup>×4×5, (-1)<sup>5</sup>×5×6, (-1)<sup>6</sup>×6×7 ....

So the general term for 2a<sub>n</sub> is  

2a<sub>n</sub> (-1)<sup>n</sup>×n×(n+1)

So the general term for a<sub>n</sub> is half that, so
we divide both sides by 2:

     (-1)<sup>n</sup>×n×(n+1)
a<sub>n</sub> = —————————————
           2

or eliminating the multiplication symbols:

     (-1)<sup>n</sup>n(n+1)
a<sub>n</sub> = ———————————
          2

Edwin</pre></font></b>