 Hi and welcome to the session. I am Shashi and I am going to help you to solve the following question. Question is in the following APs find the missing term in the boxes. The given AP is blank box 38, blank box blank box blank box minus 22. We have to find the missing terms. Let us start with the solution now. First of all we will rewrite the AP given in the question that is blank box 38, blank box. blank box blank box minus 22. Now clearly we can see the first term is missing, third term is missing, fourth term is missing and fifth term is missing. So let us assume that the first term be A1, third term be A3, fourth term be A4, fifth term be A5. So we can write that third, fourth, A1, A3, A4, A5. So we can write given AP is A1 38, A3 minus 22. Now we know nth term of AP is given by an 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. So we know second term of AP is equal to 38. So we can write a2 is equal to a plus 2 minus 1 multiplied by d. Now substituting for a2 38 we get 38 is equal to a plus d. Let us name this equation as 1. Now we are given sixth term of AP is minus 22. So we can write a6 is equal to a plus 6 minus 1 multiplied by d where a is the first term of AP and d is the common difference. Now sixth term is equal to minus 22. So we can write minus 22 is equal to a plus 50. Now let us name this equation as 2. Now we are subtracting equation 1 from equation 2. We get minus 22 minus 38 is equal to a plus 5 d minus a plus d. Now this implies minus 16 is equal to a plus 5 d minus a minus d. Now plus a minus a will get cancelled and we get minus 16 is equal to 4 d. Rearranging we get 4 d is equal to minus 16. This implies d is equal to minus 60 upon 4 or we get d is equal to minus 15. Now we know a2 is equal to a1 plus d where a1 is the first term of AP. Now we know second term of AP that is a2 is equal to 38. So we will substitute 38 for a2 and a1 d is equal to minus 15. We get a1 plus minus 15 is equal to 38. Now we get a1 is equal to 38 plus 15. This implies a1 is equal to 53. Similarly we can find a3 that is the third term is equal to a2 plus d. We know a2 is equal to 38 and d is equal to minus 15. So we get a3 is equal to 38 minus 15 or we can say a3 is equal to 23. Similarly we can find a4 is equal to a3 plus d which is equal to similarly a5 is equal to minus 7. That is it is equal to a4 plus d now a4 is equal to 8. So 8 plus minus 15 is equal to minus 7 so we get a5 is equal to minus 7. So the given AP is 53, 38, 23, 8 minus 7 minus 22. So our required missing terms are 53, 23, 8 minus 7. These are our required terms. This completes the session. Hope you understood the session. Take care and goodbye. Thank you.