Question

if sn is the sum of the first n terms of a certain sequence and sn = n(n+1)

Answer 1

sn=n(n+1)
So, s(n-1)=(n-1)n
Tn(nth term)=sn-s(n-1)=n(n+1)-n(n-1)
                                    =2n
From this you can get to whatever you actually wanted.