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If the pth term of an AP is q and the qth term is p, prove that its nth term is (p+q-n).

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  1. a+(p-1)d = q
    a+(q-1)d = p

    (p-1)d-q = (q-1)d-p
    [(p-1)-(q-1)]d = q-p
    (p-q)d = q-p
    d = (q-p)/(p-q) = -1

    Tn = Tq + (n-q)d
    = p + (n-q)(-1)
    = p+q-n

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  2. thnaks :)

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