In known sequence an, A1 = 2, the first n terms and Sn, if Sn = n ^ 2An, find an

sn=n^2an
s(n-1)=(n-1)^2*a(n-1)
sn-s(n-1)=n^2an-(n-1)^2*a(n-1) =an
(n^2-1)an=(n-1)^2a(n-1)
(n+1)an=(n-1)a(n-1)
na(n-1)=(n-2)a(n-2)
(n-1)a(n-2)=(n-3)a(n-3)
……
5a4=3a3
4a3=2a2
3a2=1a1
On both sides:
3×4×5×…… ×(n-1)n(n+1)an=1×2×3×…… ×(n-3))(n-2))(n-1)a1
n(n+1)an=2a1
an=2a1/[n(n+1)]=4/[n(n+1)].

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