If Sn denotes the sum of first n terms of an AP, prove that S30=3(S20-

1.	If Sn denotes the sum of first n terms of an AP, prove that S30=3(S20- S10)
Answer» S30 = 30/2 ( a+a+29d ) S20 = 20/2 ( a+a+19d )S10 = 10/2 ( a+a+9d )S30=3( S20 - S10 )15 ( 2a + 29d ) = 3[10(2a + 19d) - 5(2a + 9d)] 30a + 435d = 3[ 20a + 190d - 10a - 45d ] = 3[ 10a + 145d ] = 30a +435d

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