 Hello and welcome to the session, I am Asha and I am going to help you with the following question which says if the sum of three numbers in AP is 24 and their product is 440, find the numbers. Let us now begin with the solution and let the three numbers in AP be A minus D, A and A plus D. So, here the common difference is D and let this be greater than 0. Now, we are given that sum of these three numbers is equal to 24, this implies A minus D plus A plus A plus D is equal to 24 or 3A is equal to 24 which further implies that A is equal to 8. Also we are given that the product of these three numbers is equal to 440. So, this implies A minus D into A into A plus D is equal to 440, A square minus D square is equal to 440. So, A square minus D square is equal to 440 upon 8 which is 55. A square minus D square is equal to 55 or we have D square is equal to A square minus 55 and A is 8. So, 64 minus 55 this is equal to 9. So, this implies D square is equal to 9 or D is equal to plus minus 3 and since we have supposed that let D is greater than 3. So, we have D is equal to 3 and therefore, the numbers are A minus D that is 8 minus 3, 8 that is 8 and A plus D 8 plus 3 or 5, 8 and 11. So, the required answers are the three numbers in APR 5, 8 and 11 such that there is sum is 24 and product is 440. So, this completes the solution take care and have a good day.