an=4an-1+3n2n
it is a nonlinear homogeneous recurrence relation
soln format an = ah+ap ah is homogeneous soln nd ap is particular soln
homogeneous soln
characteristic equation= r-4=0
characteristic root=r=4
soln= x.rn=x.4n
particular soln
Fn= 3n2n =(cn+d )2n put this into recc reln
(cn+d )2n =4(c(n-1)+d )2n-1 +3n2n
=n(c+3)+d-2c =0
after solving c=-3 d=-6 particular soln= -(3n+6)2n
now an = ah+ap =x.4n + -(3n+6)2n
put a0=4 x=10
so ans=10.4n + -(3n+6)2n option a.
