 Hello and welcome to the session. In this session we discuss the following question which says if the p-th term of an AP is Q and the Q-th term is P, find its n-th term. So we are given the p-th term and the Q-th term of an AP, we have to find its n-th term. n-th term of an AP is given by Tn and this is equal to a plus n minus 1 into D where this a is the first term of the AP, d is the common difference of the AP. This is the key idea that we use in this question. Now let's proceed with the solution. So we are given the p-th term of an AP is equal to Q and the Q-th term of an AP is equal to P and we need to find the n-th term of an AP. Now the p-th term of the AP is given by Tp and this is equal to a plus p minus 1 into D and this is equal to Q that is we have a plus p minus 1 into D is equal to Q. Let this be equation 1. Now the Q-th term is given by TQ, this is equal to a plus Q minus 1 into D and this is given as P that is we have a plus Q minus 1 into D is equal to P. Let this be equation 2. Now we have got two equations a plus p minus 1 into D is equal to Q and a plus Q minus 1 into D is equal to P. Now we will solve both these equations for the values of a and d. Now subtracting equation 2 from equation 1 we get a plus p minus 1 into D minus a plus Q minus 1 into D this is equal to Q minus P which means a plus p minus 1 into D minus a minus Q minus 1 into D is equal to Q minus P. Now a and minus a cancels so this gives us D into P minus 1 minus Q minus 1 is equal to Q minus P or D into P minus 1 minus Q plus 1 is equal to Q minus P. Now here 1 minus 1 cancels so we have D into P minus Q is equal to Q minus P which means D is equal to minus of P minus Q upon P minus Q which gives us D is equal to minus 1. So we have got the value for D so now substituting D equal to minus 1 in equation 1 we get a plus p minus 1 into minus 1 is equal to Q which means a minus p minus 1 is equal to Q. So this gives us a is equal to Q plus p minus 1 or you can say a is equal to P plus Q minus 1 so we have got the value for a also. Now the nth term of an AP is given as Tn is equal to a plus n minus 1 into D. Now we put the values for a and d so we get Tn is equal to p plus Q minus 1 plus n minus 1 into minus 1 we say that Tn is equal to p plus Q minus 1 minus n plus 1 1 and minus 1 cancels and we get Tn is equal to p plus Q minus n. So the nth term of an AP given by Tn is equal to p plus Q minus n this is our final answer. So this completes the session hope you have understood the solution for this question.