Q22 of 176 Page 8

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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