Sir please give me a detailed solution of this question in which we have been asked to show that its (p + q)th term is zero, if the pth term of an AP is q and its q term is p.
RS Aggarwal, class 10, chapter 5A, question no 40.
If the pth term of an AP is q and its q term is p then show that its (p + q)th term is zero.
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By using nth term tn​=a+(n−1)d we have,
q=a+(p−1)d …(1)
p=a+(q−1)d  …(2)
Solving (1) and (2), we get
d=−1,a=p+q−1
∴Tp+q​=a+(p+q−1)d
=(p+q−1)+(p+q−1)(−1)
=p+q−1−p−q+1
=0