Q. 13.6( 14 Votes )

The first term of

Answer :

Given first term is ‘a’ and sum of first p terms is Sp = 0 we have to find the sum of next q terms


Total terms are p + q


So, sum of all terms minus the sum of the first p terms will give the sum of next q terms


But sum of first p terms is 0 hence sum of next q terms will be the same as sum of all terms


So, we have to find sum of p + q terms


Sum of n terms of AP is given by


Where a is first term and d is the common difference


Using the given hint


Required sum = Sp+q – Sp


Using Sn formula



Now we have to find d


We use the given Sp = 0 to find d



0 = 2a + (p – 1) d



Put this value of d in (i)


required sum







Hence proved.


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