 Hi, and welcome to the session. I am Deepika here. Let's discuss the question whether the following list of numbers is In an AP if they form an AP find the common difference D and write three more terms root 2 root 8 root 18 root 32 and so on. Let's start the solution solution are given list of numbers is root 2 root 8 root 18 root 32 and so on. We have a 2 minus a 1 is equal to root 8 minus root 2 which is equal to root 8 is 2 root 2 minus root 2. This is equal to root 2. a 3 minus a 2 root 18 minus root 8 This is equal to root 18 is 3 root 2 minus root 2 is 2 root 2 which is equal to root 2 Now a 4 minus a 3 is equal to root 32 minus root 18 root 32 is 4 root 2 minus root 18 is 3 root 2. This is equal to root 2 We find that a 2 minus a 1 is equal to a 3 minus a 2 which is again equal to a 4 minus a 3. That is a k plus 1 minus a k is the same every time. Therefore, the given list of numbers forms an AP with common difference D is equal to root 2 Now next three terms are root 32 plus root 2 which is equal to 4 root 2 plus root 2 Which is equal to 5 root 2. This is again equal to root 50 Now root 50 plus root 2 Now root 50 is 5 root 2 2 plus root 2 This is equal to 6 root 2 and 6 root 2 is equal to root 72 Now root 72 plus the common difference D which is equal to root 2. This is equal to 6 root 2 plus root 2 This is equal to 7 root 2 and 7 root 2 is equal to root 98 Hence our answer for the above list of numbers is yes They form an AP with common difference D is equal to root 2 and the next three terms are root 50 root 70 and root 70 root 72 and root 98 I Hope the question is clear to you. Bye and have a good day