If the sum of the first p terms of an A.P. is q and the sum of first q terms is p, then find the sum of first (p + q) terms.

Given: Sp = q and Sq = p

To find: Sp+q

We know that,

…(i)

Now,

…(ii)

From eq. (i) and (ii), we get

[, a2 – b2 = (a – b)(a + b)]

…(iii)

Now, putting the value of d in eq. (i), we get

…(iv)

Now, we to find Sp+q

[from (iii) & (iv)]

Sp+q = - (p+q)

Hence, the sum of first (p+q) terms is –(p + q)

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