 Hello and welcome to the session. Let us understand the following question today. A sum of Rs 700 is to be used to give 7 cash prizes to students of a school for their overall academic performance. If each prize is 20 less than its preceding prize, find the value of each of the prizes. Now let us write the solution. The value of 7 prizes forms an AP with common difference here. Common difference is equal to 20. Since it is given that each prize is 20 less than its preceding prize and it is given to us that sum of the prizes is equal to Rs 700. Now let the value of first prize be Rs A. Then D is equal to minus 20, S7 is equal to 700. Now we know Sn is equal to n by 2 multiplied by 2A plus n minus 1D. And we have to find the value of A and we have S7 is equal to 7 by 2 multiplied by 2A plus 7 minus 1 multiplied by minus 20. S7 is given to us as 700 so it implies 700 is equal to 7 by 2 multiplied by 2A plus 6 into minus 20. Which implies 700 is equal to 7 by 2. Now taking 2 common from this we get into 2 multiplied by A plus 3 into minus 20. Now here we see that this 2 and 2 gets cancelled so it implies 700 is equal to 7 multiplied by 8 minus 60. Which implies 700 is equal to 7A minus 420. Which implies 7A is equal to 700 plus 420. Which implies 7A is equal to 1120. Which implies A is equal to 1120 divided by 7. Now here we see that it gets cancelled by 160. Which implies A is equal to 160. So we have got the first term as 160. Now since it is given that each prize is 20 less than its preceding prize. So first term is equal to 160 which is equal to A1. So now A2 is equal to 160 plus D which is equal to 160 minus 20 which is equal to 140. Now similarly finding A3 is equal to 140 plus D which is equal to 140 minus 20 which is equal to 120. Now A4 is equal to 120 plus D which is equal to 120 minus 20 which is equal to 100. Now A5 is equal to 100 plus D which is equal to 100 minus 20 which is equal to 80. A6 is equal to 80 plus D which is equal to 80 minus 20 which is equal to 60. Now A7 is equal to 60 plus D which is equal to 60 minus 20 which is equal to 40. to 40. Hence, value of prizes in rupees are 160, 140, 120, 180, 60, and 40. And this is our required answer. I hope you understood the question. Bye and have a nice day.