Question 1000370
-1,2,-4,8
<pre>
{{{matrix(1,2,2nd,term)/matrix(1,2,1st,term)=2/(-1)=-2}}}

{{{matrix(1,2,3rd,term)/matrix(1,2,2nd,term)=(-4)/2=-2}}}

{{{matrix(1,2,4th,term)/matrix(1,2,3rd,term)=8/(-4)=-2}}}

So there is a common ratio of -2.  This is a geometric 
sequence with r=-2 and a<sub>1</sub>=-2.

Substitute in the formula:

a<sub>n</sub> = a<sub>1</sub>r<sup>n-1</sup>

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

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

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

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

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

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

Edwin</pre>