airthmetic progression

If m, n are natural numbers, m > n, sum of mth and nth term of an increasing AP is 2m and their product is
m^2–- n^2, then what is the (m+n)th term of the A.P.?

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asked by simmi
  1. Tn = a+(n-1)d
    Tm = a+(m-1)d
    Tn+Tm = 2a + (n+m-2)d = 2m

    T(n+m) = a+(n+m-1)d = Tn+Tm-a+d = 2m-a+d

    Hmmm. How about

    -4 -1 2 5 8 11 14 17
    a = -4 d = 3 n=3 m=5
    T3 = 2
    T5 = 8
    T3+T5 = 2+8 = 10 = 2(5)
    T3*T5 = 2*8 = 16 = 5^2-3^2

    Can't figure out how to use the product to eliminate both a and d.

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    posted by Steve

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