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If `S_n` denotes the sum of the first `n` terms of an A.P., prove that `S_(30)=3(S_(20)-S_(10))` .

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If S_(n) denotes the sum of first n terms of an AP, then prove that S_(12)=3(S_(8)-S_(4)).

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Knowledge Check

  • If S_(n) denotes the sum of first n terms of an A.P., then (S_(3n)-S_(n-1))/(S_(2n)-S_(n-1)) is equal to

    A
    2n-1
    B
    2n+1
    C
    4n+1
    D
    2n+3

  • If S_(n) is the sum of the first n terms of an A.P. then : (a) S_(3n)=3(S_(2n)-S_n) (b) S_(3n)=S_n+S_(2n) (c) S_(3n)=2(S_(2n)-S_(n) (d) none of these

    A
    `S_(3n)=3(S_(2n)-S_(n))`
    B
    `2.S_(3n)=S_(n)+S_(2n)`
    C
    `S_(3n)=2(S_(2n)-S_(n))`
    D
    none of these

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    Let S_(n) denote the sum of the first n terms of an A.P.. If S_(4)=16 and S_(6)=-48 , then (S_(10))/(-80) is equal to ____________.

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