4, 4¼, 4½, 5
4, 4.25, 4.5, 5

,  a(1)=4, a(2)=4.25, n=3,4,5,...

 





 

Solve this system:

 

Multiply both equations through by 100 to clear decimals



Divide both equations through by 25





To eliminate p multiply first equation through by -18
and second equation through by 17



Add term by term

q = 16

Substitute 16 for q in

   17p+16q = 18
17p+16(16) = 18
   17p+256 = 18
       17p = -238
         p = -14

So the recursion formula is

an = -14an-1 + 16an-2, a(1)=4, a(2)=4.25, n=3,4,5,...

Edwin