a2 = 1/[ 1-(- 1/3]= 3/4

a3= 1/[ 1-3/4]=4

a4 = 1/[ 1-4]=- 1/3

It can be seen that a 1=a4. This is a cycle.

That is to say a1= a4 = a7 = a10 = a (3x+1) =-1/3.

a2009=a(3*669+2)=a2=3/4

So 2009 =3/4