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If Sn=n P+(n(n-1))/2Q ,w h e r eSn denot...

If `S_n=n P+(n(n-1))/2Q ,w h e r eS_n` denotes the sum of the first `n` terms of an A.P., then find the common difference.

Text Solution

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The correct Answer is:
Q
`S_(n)=nP+(n(n-1))/2Q`
`=n/2[2P+(n-1)Q]`
Compairing with
`S_(n)=n/2[2a+(n-1)d]`
d=Q
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Knowledge Check

  • If S_(n) = nP + (1)/(2)n (n - 1)Q where S_(n) denotes the sum of the first n terms of an A.P., then the common difference is

    A
    P + Q
    B
    2P + 3Q
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    Q

  • If S_(n)=nP+(n(n-1)Q)/(2) , where S_(n) denotes the sum of the first terms of an AP, then the common difference is:

    A
    A)`P+Q`
    B
    B)`2P+3Q`
    C
    C)`2Q`
    D
    D)`Q`

  • The sum of first n terms of an A.P. is 5n ^(2)+ 4n, its common difference is :

    A
    9
    B
    10
    C
    3
    D
    `-4`

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