If the p-th term of an A.P. is q and the q-th term is p, then its n-th term is:
Answer: A
Let the A.P. have first term 'a' and common difference 'd'. \(a_p = a+(p-1)d = q\) and \(a_q = a+(q-1)d = p\). Subtracting the two equations gives \((p-1-q+1)d = q-p \Rightarrow (p-q)d = -(p-q) \Rightarrow d = -1\). Substituting d=-1 into the first equation: \(a+(p-1)(-1)=q \Rightarrow a-p+1=q \Rightarrow a = p+q-1\). The nth term is \(a_n = a+(n-1)d = (p+q-1) + (n-1)(-1) = p+q-1-n+1 = p+q-n\).