if the pth term of an AP is q and its qth term is p then show that (p+q)th term is zero

if the pth term of an AP is q and its qth term is p then show that (p+

1.	if the pth term of an AP is q and its qth term is p then show that (p+q)th term is zero
Answer» Let a be the first term and d be the common differencepth\xa0term = a +(p - 1)d = q(given)-----(1)qth\xa0term = a +(q - 1) d = p(given)-----(2)subtracting (2) from (1)(p-q)d=q-p(p-q)d=-(p-q){tex}\\therefore{/tex}\xa0d = -1putting d=-1 in (i)a - (p - 1) = q{tex}\\therefore{/tex}\xa0a=p+q-1{tex}\\therefore{/tex}\xa0(p + q)th term = a + (p + q - 1)d= (p + q - 1) - (p + q - 1) = 0