Question

Solve
Fn=10fn-1 +25 fn-2
where fn=3 and F1=17​

Answer 1

Hence, the roots are −

x1=3 and x2=2

The roots are real and distinct. So, this is in the form of case 1

Hence, the solution is −

Fn=axn1+bxn2

Here, Fn=a3n+b2n (As x1=3 and x2=2)

Therefore,

1=F0=a30+b20=a+b4=F1=a31+b21=3a+2b

Solving these two equations, we get a=2 and b=−1

Hence, the final solution is −

Fn=2.3n+(−1).2n=2.3n−2n