Q5 of 23 Page 1

Attempt any two of the following subquestions:

If the sum of first p terms of an A.P. is equal to the sum of first q terms, then show that the sum of its first (p + q) terms is zero where p#q.

Sum of n terms of AP is given as:


Sum of p terms, Sp is given as:



Sum of q terms, Sq is given as:



Now, its given that Sp = Sq


⇒


⇒ 2ap + pd(p - 1) = 2aq + qd(q - 1)


⇒ 2a(p - q) + d(p2 - q2) = (p - q)d


⇒ 2a(p - q) + d(p - q)(p + q) = (p - q)d


⇒ 2a + d(p + q) = d


⇒ 2a = - d(p + q - 1) ……………..(1)


Sum of (p + q) terms :


Sp + q =


From eq(1) putting value of 2a,


Sp + q =


Sp + q = 0.


Hence proved.


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