 Hi and welcome to the session I am Deepika here. Let us discuss the question whether the following form an AP if they form an AP find the common difference D and write three more terms minus one by two minus one by two minus one by two minus one by two and so on. We know that the given list of terms A1, A2, A3 so on forms an AP if the difference of a term and its preceding terms is always constant. This constant is called the common difference of AP. Let us use this key idea to solve up a question. Let us start the solution. The given list of terms is minus one by two minus one by two minus one by two and so on. We have A2 minus A1 is equal to minus one by two minus of minus one by two which is equal to zero again. A3 minus A2 is equal to minus one by two minus minus one by two which is again equal to zero. Again A4 minus A3 is equal to minus 1 by 2 minus minus 1 by 2 which is equal to 0. That is, A k plus 1 minus A k is the same every time that is it is constant. So, the given list of numbers forms an AP with common difference D is equal to 0. The next three terms are minus 1 by 2 plus 0 which is again minus 1 by 2, again minus 1 by 2 plus 0 which is equal to minus 1 by 2 and again minus 1 by 2 plus 0 because the common difference D is equal to 0. So, the next three terms are minus 1 by 2 minus 1 by 2 and minus 1 by 2 hence the answer for the above question is yes the given list of terms form an AP with the common difference D is equal to 0 and the next three terms are minus 1 by 2 minus 1 by 2 and minus 1 by 2. I hope you have enjoyed the session, bye and take care.