If Sn denotes the sum of the first n terms of an AP, prove that S30=3(

1.	If Sn denotes the sum of the first n terms of an AP, prove that S30=3(S20-S10).
Answer» Sn=n/2(2a+(n-1)d)S30=30/2(2a+29d)S30=30a+435d... (1)S20=20/2(2a+19d)S20=20a+190d....(2)S10=10/2(2a+9d)S10=10a+45d....(3)3(S20-S10)=3(20a+190d-10a-45d) =3(10a+145d) =30a+435d=S30 (from 1) So, S30=3(S20-S10) Hence proved.

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