Answer :

given an AP whose sum of n terms is n2p and same AP with m terms whose sum is m2p

To prove: Sp = p3


we know that the sum of AP is given by the formula:



substituting the values in the above equation, we get


…. (i)


Similarly, for series with m terms


…(ii)


Subtracting (ii) from (i) we get


d = 2p


substituting d in (i) we get


a = p


Now using the sum formula for AP consisting of p terms we get



Substituting the values in the above equation



SP = p3


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