 Hi and welcome to the session. I am Shashi and I am going to help you to solve the following question. Question is an AP consists of 50 terms of which third term is 12 and last term is 106. Find the 29th term. Let us start with the solution now. We know in the question the AP consists of total 50 terms. So the last term of the AP would be 50th term. Now we also know that nth term 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. Now we are given in the question that third term of the AP is 12. So we can write a3 is equal to 12. Also we know a3 is equal to a plus 3 minus 1 multiplied by d where a is the first term of the AP and d is the common difference. Now a3 is 12. So we will substitute the value of a3 here. Now we get 12 is equal to a plus 2d. Let us name this equation as 1. Now we are given last term of the AP is 106. This implies last term of the AP is 50th term. So 50th term of AP is equal to 106. So we can write 50th term is also equal to a plus 50 minus 1 multiplied by d. 50th term is equal to 106. So we will write 106 is equal to a plus 4090. Now let us name this equation as 2. Now subtracting equation 1 from equation 2 we get 106 minus 12 is equal to a plus 4090 minus a plus 2d. Now this implies 94 is equal to a plus 4090 minus a minus 2d. Now a and a will get cancelled. So we get 94 is equal to 4070 or we can write 4070 is equal to 94. This implies d is equal to 94 upon 47. 47 to the is 94. So d is equal to 2. Now substituting d is equal to 2 in equation 1 we get a plus 2 multiplied by 2 is equal to 12. This implies a is equal to 12 minus 4. This further implies a is equal to 8. Now we are having d is equal to 2 and a is equal to 8 where a is the first term of AP and d is the common difference of AP. Now we have to find the 29th term. We hope 29th term of the AP is equal to 8 plus 29 minus 1 multiplied by d. Now 29th term is equal to 8 plus 28 multiplied by d is equal to 2. So we get 29th term is equal to 8 plus 56 or we get 29th term is equal to 64. So we can write 29th term of AP is 64. So our required answer is 64. This completes the session. Hope you understood the session. Take care and goodbye.