The known sequence {an} satisfies A1 = 1; an = a1 + 2A2 + 3a3 +... + (n-1) a (n-1); (n > = 2); find the general term formula

The known sequence {an} satisfies A1 = 1; an = a1 + 2A2 + 3a3 +... + (n-1) a (n-1); (n > = 2); find the general term formula

A2 = a1 + 2A2 = 1 + 2A2, then A2 = - 1An = a1 + 2A2 + 3a3 +... + (n-2) a (n-2) + (n-1) a (n-1) a (n-1) = a1 + 2A2 + 3a3 +... + (n-2) a (n-2) subtraction: an-a (n-1) = (n-1) a (n-1), that is, an = Na (n-1), so an / a (n-1) = Nan = [an / a (n-1)] [a (n-1) / a (n-2)]... [A3 / A2] a

If the sequence {an} satisfies a1 + 2A2 + 3a3 + +Nan = n (n + 1) (n + 2) (n ∈ n *), find the general formula of {an}

∵a1+2a2+3a3+… +nan=n（n+1）（n+2）（n∈N*），∴a1+2a2+3a3+… +(n-1) an-1 = (n-1) n (n + 1) (n ∈ n *), by subtracting the two formulas, we obtain Nan = n (n + 1) (n + 2) - (n-1) n (n + 1) (n ∈ n *), an = 3N + 3