A very common recursion formula is of this form:

, where a,b, and c are constants:

Substitute n=1





Substitute n=2





Substitute n=3





We will find a,b, and c from this system:



Subtracting the 1st equation from the 2nd equation



Subtracting the 2nd equation from the 3rd equation



So now we have this system:



Subtracting the first equation from the second:





Substitute in 12a+b=10

12(1)+b=10
   12+b=10
      b=-2

Substitute in 16a+b+c=14

16(1)+(-2)+c=14
      16-2+c=14
        14+c=14
           c=0

So recursion formula:





Now we test the recursion formula to see if 







So this is the correct recursion formula.

So we use it to find 





   <--answer

Edwin