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the ratio of the sum to terms p and q terms of an a.p. is psquare:qsquare. prove that the common difference of the a.p. is twice the first term

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p/2 (2a+(p-1)d)
------------------- = p^2/q^2
q/2 (2a+(q-1)d)

2a+pd-d
---------- = p/q
2a+qd-d

q(2a+pd-d) = p(2a+qd-d)
pqd + q(2a-d) = pqd + p(2a-d)
(p-q)(2a-d) = 0

So, either p=q or d=2a

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