Q. 154.1( 11 Votes )

If the sum of p t

Answer :

The sum of n terms of an AP is given by


Where a is the first term and d is the common difference


Given that Sp = q and Sq = p








Subtract (i) from (ii) that is (ii) – (i)




Using a2 – b2 = (a + b)(a – b)





We have to show that Sp+q = -(p + q)






Using (m) and (n)


Sp+q = Sp + Sq + pqd


= q + p + pqd


Substitute d from (iii)



= (p + q) – 2(p + q)


= -(p + q)


Now we have to find sum of p – q terms that is Sp-q






Using (m) and (n)





Substitute d from (iii)








Hence sum of p – q terms is


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