If Sn denotes the sum of first n terms of an A.P , prove that S30=3(S2

1.	If Sn denotes the sum of first n terms of an A.P , prove that S30=3(S20 -S10)
Answer» Let a be the first term and d be the common difference of the given AP.Then sn = n/2(2a + (n-1)d).\xa0LHS :S30 = (30/2)(2a + (30 - 1)d) = 15(2a + 29d) = 30a + 435d. ---------------- (1).RHS:(S20 - S10) = (20/2)(2a + (20 - 1) * d) - (10/2)(2a + (10 - 1) * d) = 10(2a + 19d) - 5(2a + 9d) = 20a + 190d - 10a - 45d = 10a + 145d 3(S20 - S10) = 3(10a + 145d) = 30a + 435d ------------- (2)Therefore From (1) and (2), It is proved that S30 = 3(S20 - S10).LHS = RHS.

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