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If the sum of n terms of an A.P. is (p n...

If the sum of n terms of an A.P. is `(p n+q n^2)`, where p and q are constants, find the common difference.

Text Solution

Verified by Experts

Given `S_n=Pn+Qn^2`
`:. T_n=S_n-S_(n-1)`
`=Pn+Qn^2-[P(n-1)+Q(n-1)^2]`
`=P-Q+2nQ`
...
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Knowledge Check

  • If the sum of n terms of an A.P. is an(n - 1) where a ne 0 , then sum of squares of these terms is

    A
    `a^(2)n^(2) (n + 1)^(2)`
    B
    `(2)/(3) a^(2) n (n + 1) (2n + 1)`
    C
    `(2)/(3) a^(2) n (n - 1) (2n - 1)`
    D
    none

  • If in an A.P. the ratio of the sum of m terms and n terms is m^(2) : n^(2) then if a is first term and d the common difference, then

    A
    a = 2d
    B
    a = d
    C
    d = 2a
    D
    none of these

  • If the sum of the first n terms of an A.P. is pn+ qn^(2) then its common difference is

    A
    p-q
    B
    p+q
    C
    2q
    D
    2p

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