Answer :

Given first term is ‘a’ and sum of first p terms is S_{p} = 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 = S_{p+q} – S_{p}

Using S_{n} formula

Now we have to find d

We use the given S_{p} = 0 to find d

⇒ 0 = 2a + (p – 1) d

Put this value of d in (i)

⇒required sum

Hence proved.

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