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 S_{p} = q and S_{q} = p

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

Using a^{2} – b^{2} = (a + b)(a – b)

We have to show that S_{p+q} = -(p + q)

Using (m) and (n)

⇒ S_{p+q} = S_{p} + S_{q} + 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 S_{p-q}

Using (m) and (n)

Substitute d from (iii)

Hence sum of p – q terms is

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