 Hello and welcome to the session. I am Asha and I am going to help you with the following question that says how many terms of the AP minus 6 minus 11 upon 2 minus 5 are needed to give the sum minus 25. Let us now begin with the solution. The given AP is minus 6 minus 11 upon 2 minus 5 and so on. And here the first term is equal to minus 6 and the common difference is equal to minus 11 upon 2 minus of minus 6 which is equal to minus 11 upon 2 plus 6 which is 1 upon 2. Now let terms of the given AP gives minus 25 that is Sn is equal to minus 25. Now the formula of Sn is n upon 2 into 2A plus n minus 1 into d. This is equal to minus 25 or minus 1 into d is half. This is equal to minus 25 or minus 12 plus n upon 2 minus half is equal to minus 25. N upon 2 into n upon 2 minus 25 upon 2 is equal to minus 25 or n upon 4 into n minus 25 is equal to minus 25 or we can say that further. n square minus 25 n is equal to minus 100 upon cross multiplying and opening the brackets or n square minus 25 n plus 100 is equal to 0. Now by splitting the middle term this expression can further represent us n square minus 20 n minus 5 n plus 100 is equal to 0. Now taking n common from the first two terms and minus 5 common from the last two terms we have into n minus 20 minus 5 into n minus 20. n minus 20 into n minus 5 is equal to 0. Here also we have 0 sorry. Now if the product of two numbers is equal to 0 then at least one of them is 0 this implies either n minus 20 is equal to 0 or n minus 5 is equal to 0 this implies 25 or 20. Both the values of n give the required sum hence answer is the value of n is 5 or 20. So this completes the session hope you enjoyed it take care and have a good day.