 Hi and welcome to the session, I am Shashi and I am going to help you to solve the following question. Question is, find the 34th term of an AP whose 11th term is 38 and 16th term is 73. Let us start with the solution now, let the required AP be A1, A2, A3 till A n. Now we also know that the nth term of the AP is given by the formula A n is equal to A plus n minus 1 multiplied by d where A is the first term of AP and d is the common difference between the two consecutive terms of the AP. Now we have given in the question that 11th term of AP is 38, so we can write 11th term is equal to A A1 plus 11 minus 1 multiplied by d where A1 is the first term of the AP and d is the common difference between the two consecutive terms of the AP. Now 11th term is equal to 38 as given in the question, so we can write 38 is equal to A1 plus 10 d. Now another addition given in the question is 16th term is 73, 16th term of AP is 73 otherwise 16th term is equal to A1 plus 16 minus 1 multiplied by d. Now 16th term is equal to 73, so we can write 73 is equal to A1 plus 15 d where A1 is the first term of the AP and d is the common difference of the AP. Now let us name this equation as 1 and this equation as 2. Now the tracking equation 2 from equation 1 we get 38 minus 73 is equal to A1 plus 10 d minus A1 plus 15 d. Now this implies minus 35 is equal to A1 plus 10 d minus A1 minus 15 d. Now this implies minus 35 is equal to A1 and A1 will get cancelled is equal to minus 15 d or we can write minus 15 d is equal to minus 35 this implies d is equal to minus 35 upon minus 5. Now we get d is equal to 7 minus n minus sign will get cancelled and we know 5 7 of 35 so d is equal to 7. Now we will substitute this value of d in equation 1 to get the value of A1. Now substituting d is equal to 7 in equation 1 we get A1 plus 10 multiplied by 7 is equal to 38 this implies A1 is equal to 38 minus 17 this implies A1 is equal to minus 32. Now we know the first term of the AP and the common difference of the AP. So we can calculate the 31st term. Now 31st term is equal to A1 plus 31 minus 1 multiplied by d we know 31st term we have to find out is equal to A1 is equal to minus 32 plus 30 multiplied by 7 as d is equal to 7. Now we get 31st term is equal to minus 32 plus 210. Now we get 31st term is equal to 178. So we can write 31st term of AP is 178 so our required answer is 178. This completes the session hope you understood the session take care and goodbye.