 Hi and welcome to the session, I am Deepika here. Let's discuss a question. In the following situation, does a list of numbers make an automatic progression and why? Situation is, the cost of digging a well after every meter of digging, when it costs rupees 150 for the first meter and rises by rupees 50 for each subsequent meter. Let us first understand what is the meaning of an automatic progression. An automatic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding number except for the first term. Now let's start the solution. Solution, the fixed cost of digging for the first meter rupees 150. Therefore the cost of digging for the second meter is rupees 150 plus rupees 50 which is equal to rupees 200. Now the cost of digging for the third meter is equal to rupees 200 plus rupees 50 which is equal to rupees 250. Now the cost of digging for the fourth meter is equal to rupees 250 plus rupees 50 which is equal to rupees 300. Thus we have the terms as follows 150, 200, 250, 300 and so on. Now see 200 is obtained by adding a 50 to 150. Again 250 is obtained by adding 50 to 200. Again 300 is obtained by adding 50 to the preceding term that is 250. Therefore it forms an AP that is arithmetic progression. Each term is obtained by adding a fixed number. In this case it is a 50 rupees 50 is a fixed number to the preceding number. Hence our answer is yes above situation forms an AP and terms are 150, 200, 250, 300 and so on. Forms an AP. So this is our answer. I hope the question is clear to you. Bye and have a nice day.