If pth term of an A.P.is q and the qth term is p prove that its nth te

1.	If pth term of an A.P.is q and the qth term is p prove that its nth term is (p+q-n)
Answer» Let a be the first term and d be the common difference of the given A.P. Then,pth term = q {tex}\\Rightarrow{/tex}a + (p-1) d = q ...(i)qth term = p {tex}\\Rightarrow{/tex}a + (q-1) d = p ...(ii) Subtracting equation (ii) from equation (i), we get(p - q) d = (q - p) {tex}\\Rightarrow{/tex}\xa0d = -1Putting d = - 1 in equation (i), we geta + ( p-1) × (-1) = q⇒ a = (p + q - 1)\xa0nth term = a + (n -1 )d= (p + q - 1)+ (n -1) × (-1)= p + q - 1 -n + 1= (p + q - n)

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