The common difference of an A.P., the sum of whose n terms is Sn, is

an is the nth term of an A.P and a n–1 is the (n–1)th term of an A.P,


d = common difference, Sn = sum of n terms of an A.P


d= an – an–1


But an= Sn – Sn–1


And an–1= Sn–1 – Sn–2


So d= Sn – Sn–1 – (Sn–1 – Sn–2)


d= Sn – 2 Sn–1 + Sn–2

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