 Hi and welcome to the session. Let us discuss the following question. Question says, find the number of terms in each of the following APs. Given AP is 18, 15, 1 upon 2, 13, till minus 47. First of all let us understand that nth term of an AP is equal to a plus n minus 1 multiplied by d. Here a n is the nth term of AP, a is the first term of AP and n is the total number of terms given in AP and b is the common difference. This is the key idea to solve the given question. Now let us start with the solution. AP given in the question is 18, 15, 1 upon 2, 13, till minus 47. Now let us assume that total number of terms in the given AP is n. Let nth term is equal to minus 47 and we know nth term is given by a plus n minus 1 multiplied by d. This we have already mentioned in key idea. nth term is equal to first term plus n minus 1 multiplied by d, where d is the common difference. Now nth term of AP is equal to minus 47. First term clearly we can see is equal to 18. So we can write a is equal to 18 and common difference is given by subtracting two consecutive terms. So d is equal to 15, 1 upon 2 minus 18. Now this is further equal to 31 upon 2 minus 18. Now subtracting these two terms by taking the LCM we get 31 minus 36 upon 2. Now this is further equal to minus 5 upon 2. So we get common difference of AP is equal to minus 5 upon 2. Now let us name this expression as 1. Now substituting corresponding values of a n, a and d in this expression we get minus 47 is equal to 18 plus n minus 1 multiplied by minus 5 upon 2. Now subtracting 18 from both the sides we get minus 47 minus 18 is equal to n minus 1 multiplied by minus 5 upon 2. Now this is further equal to minus 65 is equal to n minus 1 multiplied by minus 5 upon 2. Now this implies minus 65 multiplied by 2 upon minus 5 is equal to n minus 1. Here we have multiplied both the sides by 2 upon minus 5. Now minus n minus 5 will cancel each other and we know pi is multiplied by 13 is equal to 65. Now we know 13 multiplied by 2 is equal to 26. So we can write 26 is equal to n minus 1. Now adding 1 on both the sides we get 26 plus 1 is equal to n. Now 26 plus 1 is equal to 27. So we can write 27 is equal to n or we can simply write it as n is equal to 27. We know n is the total number of terms in the given AP. So total number of terms in the given AP is 27. So 27 is our required answer. This completes the session. Hope you understood the session. Take care and keep smiling.