 Hello and welcome to the session, let us discuss the following question, question says, check whether minus 150 is a term of the AP 11852. Now let us start with the solution, given AP is 11852, where clearly we can see first term of the AP is 11, so we can write first term that is a is equal to 11. Now let us find out common difference, common difference that is d is equal to 8 minus 11 which is equal to minus 3 and we also know that nth term that is an is equal to a plus n minus 1 multiplied by d. Now we have to check if minus 150 is a term of AP 11852. Now let us assume that nth term of the given AP is equal to minus 150. Now let us name this expression as 1, now substituting corresponding values of a n, d and a in this expression we get minus 150 is equal to 11 plus n minus 1 multiplied by minus 3. Now subtracting 11 from both the sides we get minus 150 minus 11 is equal to n minus 1 multiplied by minus 3. Now we know minus 150 minus 11 is equal to minus 161 minus 161 is equal to n minus 1 multiplied by minus 3. Now dividing both sides by minus 3 we get minus 161 upon minus 3 is equal to n minus 1. Now minus n minus time will cancel each other and we get 161 upon 3 is equal to n minus 1. Now adding 1 on both the sides we get 161 upon 3 plus 1 is equal to n. Now we will add these two terms by taking their LCM. We get 161 plus 3 upon 3 is equal to n. This is further equal to 164 upon 3 is equal to n or we can simply write it as n is equal to 164 upon 3. Now this can be written as 54 2 upon 3. Now clearly we can see value of n is not a natural number so minus 150 is not a term of the given AP. So our required answer is no minus 150 is not a term of the given AP. This completes the session. Hope you understood the session. Take care and have a nice day.