Using mathematical induction, the numbers a_n 's are defined by, a₀=1, a_ n+1 =3 n^2+n+a_n,(n 0) . Then, a_n is equal to

Step-by-step solution

aligned & Given, a₀=1, a_ n+1 =3 n^2+n+a_n & a₁=3(0)+0+a₀=1 & and a₂=3(1)^2+1+a₁=3+1+1=5 aligned From option (b), array ll Let & P(n)=n^3-n^2+1 & P(0)=0-0+1=1=a₀ and & P(1)=1^3-1^2+1=1=a₁ & P(2)=(2)^3-(2)^2+1=5=a₂ array Hence, option (b) is correct.