Q15 of 47 Page 1

If Sn, denotes the sum of first n terms of an A.P., prove that S12 = 3(S8-S4)

Let a be the first term and d be the common difference of A.P.

We know that


…………….(1)


…………….(2)


…………….(3)


To prove: S12 = 3(S8-S4)


Solving RHS,


RHS = 3(S8-S4)


= 3[(8a + 28d)-(4a + 6d)] (From eq (2) and (3))


= 3[4a + 22d]


= 12a + 66d


From eq(1),


RHS = 12a + 66d = S12 = LHS


Hence proved.


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