If Sn = n2p and in an A.P., prove that Sp = p3
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