Multiple Choice Questions on If Sn nP n n 1 2 where Sn denotes the sum of the first n terms of an AP then the common di........... for NDA Exam Preparation

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Multiple Choice Questions

If Sn nP n n 1 2 where Sn denotes the sum of the first n terms of an AP then the common di...........

Mathematics (NDA) Arithmetic progression
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    If Sn = nP + n(n - 1) / 2, where Sn denotes the sum of the first n terms of an AP, then the common difference is -

    P+Q

    Incorrect Answer

    2P+3Q

    Incorrect Answer

    2Q

    Incorrect Answer

    Q

    Correct Answer
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    Explanation:

    Sn = nP + n(n−1)Q / 2

    Put n= n-1
    Sn-1 = (n-1)P + (n−1)(n−2)Q / 2
    Sn – Sn-1 = an = nP – (n-1)P + n(n−1)Q / 2  –(n−1)(n−2) Q / 2
    = P + Q(n−1)(n-n+2)/2
    an = P + Q(n-1)
    Put n = 1 in Sn
    S1 = a = P
    ∴ P + Q(n-1) = P + (n-1)d 
    ∴ d = Q

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