 Hi and welcome to the session. My name is Shashi and I am going to help you to solve the following question. Question is, in the following APs, find the missing terms in the boxes. Second part is, black box 13, black box 3. First of all, let us understand the key idea to solve the given question. The LF term of an AP a1, a2, a3, a4 is given by an is equal to a plus n minus 1 multiplied by d, where a is the first term of the AP and d is the common difference. d is given by a2 minus a1, d is equal to a3 minus a2, d is equal to a4 minus a3 and so on. That is, d is equal to the difference between the two consecutive terms of the AP. These consecutive terms can be any of the consecutive terms of AP. So, this implies d remains constant. Let us start with the solution now. First of all, we will rewrite the AP given in the question, that is, black box 13, black box. We have to find the first term of the AP and the third term of the AP. Now, let us assume that the first and the third missing terms of AP are x and y. Now, the given AP will become x13 y3. Now, we know common difference d always remains constant in AP. So, we can write common difference d is equal to y minus 13 and also it is equal to 3 minus y. We can write y minus 13 is equal to 3 minus y. This implies y plus y is equal to 3 plus 13. This implies 2y is equal to 16. This further implies y is equal to 16 upon 2, that is equal to 8. So, we get y is equal to 8. So, the third missing term is 8. Now, the given AP is 13, 8, 3. Now, we know by key idea, nth term of AP is equal to a plus n minus 1 multiplied by d, where d is the common difference. a is the first term of the AP. Now, we know a is equal to that is the first term of AP is equal to x and common difference that is d is equal to 8 minus 13 is equal to minus 5. Now, we know a2 is equal to a plus 2 minus 1 multiplied by d. This implies a2 is equal to, we know a is equal to x. So, we will substitute x in place of a. 2 minus 1 is 1 multiplied by d and d is equal to minus 5. So, we will replace d by minus 5. Now, we know second term in AP is equal to 13. So, we get a2 is equal to 13. So, we can write 13 is equal to x minus 5. Now, this implies 13 plus 5 is equal to x. This implies 18 is equal to x or we get x is equal to 18. So, the first missing term of AP is 18. Now, the given AP is 18, 13, 8, 3. So, our required answer is 18 for the first box and 8 for the second blank box. This completes the session. Hope you understood the session. Take care and goodbye.