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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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

-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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