 Hi and welcome to the session. I am Deepika here. Let's discuss the question. In the following situation, does the list of numbers involved make an arithmetic progression and why? The amount of money in the account every year when Rs. 10,000 is deposited at compounding trust at 8% per annum. Let's start the solution. We know that an arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except for the first term. And also amount for annum is given by an is equal to P into 1 plus r over 100 raised to power n, where P is the principal, r is the rate of interest. So we will find the terms according to the given situation and we will see whether they form an arithmetic progression or not. Let's start the solution using the key idea. Solution. Here P is given to us through P is 10,000, r is given to us is equal to 8%. Therefore, amount for first year is equal to that is 10,001 plus r that is 8 upon 100 raised to power 1 which is equal to 2000 into 108 over 100. Again, amount for second year is equal to 10,000 into 1 plus 8 over 100 raised to power 2. Similarly, amount for third year is equal to 10,000 into 1 plus 8 over 100 raised to power 3. Therefore, we have the terms as follows 1 plus 8 over 100, 10,000, 1 plus 8 over 100 raised to power 2 which was the amount for the second year and next is 10,000, 1 plus 8 over 100 raised to power 3 and so on. Now we see that sum is not obtained by the number of preceding terms. Therefore, it does not form an AP. So for the above situation is no, the above situation does not form an AP and amounts are 10,001 plus 8 over 100 raised to power 2, 10,001 plus 8 over 100 raised to power 3. The question is clear to you, buy and have a nice day.