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

1.	If Sn, denote the sum of first n, terms of an A. P, prove that S30=3(S20-s10)
Answer» Let a be first term and d be common difference, thenS30\xa0={tex}\\frac{30}{2}{/tex}( 2a + 29d){tex}= 15(2a + 29d){/tex}.....(i)3(S20- S10) = 3 [{tex}\\;\\frac{20}2{/tex} (2a + 19d) - {tex}\\;\\frac{10}2{/tex}(2a + 9d)]{tex}= 3[10 (2a + 19d) - 5(2a + 9d)]{/tex}{tex}= 3[20a + 190d - 10a - 45d]{/tex}{tex}= 3[10a + 145d]{/tex}{tex} = 15[2a + 29d]{/tex} ...(ii)From (i) and (ii){tex}\\therefore{/tex}\xa0Hence S30 = 3(S20 - S10)

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