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if pth term of an AP is q and qth term of an AP is p then prove that its nth term is p+q-1

    • Posted by Nitika Garg 5 years, 5 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 5 years, 5 months ago

     

    Let first term be a and common difference be d.

    pth term = a + (p-1)d = q -----(i)

    qth term = a + (q-1)d = p -----(ii)

    (ii) - (i) gives

    (q - p)d = p - q or d = -1

    (i) gives  a = q - (p-1)d = q - (p-1)(-1) = q + p - 1

    Hence,

    nth term = a + (n-1)d
    = q + p -1 + (n-1)(-1)
    = q + p -1 + n +1
    = p + q - n

    1Thank You

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