 Hi and welcome to the session. My name is Joshy and I am going to help you to solve the following question. Question is, for what value of N are the Nx terms of two APs, 63, 65, 67 and 3, 10, 17 equal? First of all, let us understand that the Nx term of an AP with first term A and the common difference D is given by An is equal to A plus N minus 1 multiplied by D. This is the key idea to solve the given question. Now let us start with the solution. AP given to us is 63, 65, 67. This is the first AP given to us. So our first term of this AP is equal to 63 and common difference D is equal to 2. Now Nx term of this AP is given by An is equal to A plus N minus 1 multiplied by D where A is the first term and D is the common difference as we have already understood this in key idea. Now we will substitute for A, 63 and we will substitute for D, 2. So we get An is equal to 63 plus N minus 1 multiplied by 2. On simplifying we get An is equal to 63 plus 2N minus 2. This implies Nx term is equal to 61 plus 2N for this AP. Now the other given AP is 3, 10, 17. Now clearly the first term of this AP is equal to 3. So we can write first term as A is equal to 3 and the common difference is equal to 7 for this AP. Now we know Nx term is equal to A plus N minus 1 multiplied by D as we have read in key idea. Now we can write An is equal to 3 plus N minus 1 multiplied by 7 substituting for An D. Now this implies An is equal to 3 plus 7N minus 7. This implies Nx term of this AP is equal to 7N minus 4. Now we have to find the value of N for which Nx terms of the two given APs are equal. Therefore we can write 61 plus 2N is equal to 7N minus 4. This is the Nx term for the first AP and this is the Nx term for the second AP. Now simplifying we get 7N minus 2N is equal to 61 plus 4. This implies 5N is equal to 65. Now this further implies N is equal to 65 upon 5. This implies N is equal to 13. So the Nx terms of the two given APs are equal for N is equal to 13. So our required answer is 13. This completes the session. Goodbye and take care.