Given, a0=1, an+1=3n2+n+an ...(i) From Eq.(i), we get a1=3(0)2+0+a0=1 a2=3(1)2+1+a1=3+1+1=5 a3=3(2)2+2+a2=12+2+5=19 Now, check the option for n=3 which expression satisfy by a3=19 Option (b),an=n3−n2+1 Put n=3, then a3=(3)3−(3)2+1=27−9+1=19 ∴an=n3−n2+1