 Hello and welcome to the session. Let us understand the following question which says in a potato raise a bucket is placed at the starting point which is 5 meter from the first potato and the other potatoes are placed 3 meter apart in a straight line. There are 10 potatoes in the line. See figure 5.6. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run? Hint. To pick up the first potato and the second potato the total distance in meters run by a competitor is 2 multiplied by 5 plus 2 multiplied by 5 plus 3. Now let us proceed on to the solution. Now here is the figure. This is the bucket of potatoes and competitor first has to run 5 kilometer to pick up the first potato then he she comes back then again she has to run till this point to pick up the second potato and so on she has to pick up the 10 potatoes and we have to find the total distance the competitor takes in picking up 10 potatoes one at a time to place it in the bucket. Here we can see that competitor first time she runs 5 meter to pick the potato and back 5 meter so we can write D1 is equal to 2 multiplied by 5 meter where D1 is the distance run by competitor to pick up the first potato. Similarly D2 the distance run by the competitor to pick up the second potato is equal to 2 multiplied by 5 plus 3 meter. D3 the distance run by the competitor to pick up the third potato is equal to 2 multiplied by 5 plus 2 multiplied by 3 meter. Similarly D4 the distance run by the competitor to pick up the fourth potato is equal to 2 multiplied by 5 plus 3 multiplied by 3 meter so on and lastly we get D10 is equal to distance run by the competitor to pick up the 10th the last potato which is equal to 2 multiplied by 5 plus 9 multiplied by 3 meter. Therefore total distance run by the competitor to pick up the 10 potatoes is equal to D1 plus D2 plus D3 so on till D10 which is equal to 2 multiplied by 5 plus 2 multiplied by 5 plus 3 plus 2 multiplied by 5 plus 2 multiplied by 3 so on till 2 multiplied by 5 plus 9 multiplied by 3. Now here we can see that 2 is common in all the terms so taking 2 common which is equal to 2 multiplied by 5 plus 5 plus 3 plus 5 plus 2 multiplied by 3 so on till 5 plus 9 multiplied by 3. Now these are the different terms so we can take out 5 outside so we get here 5 plus 5 plus 5 plus 5 so on till 5 till 10 times plus 3 plus 2 multiplied by 3 plus 3 multiplied by 3 so on till 9 multiplied by 3 which is equal to 2 multiplied by when 5 is added 10 times we get 5 multiplied by 10 which is equal to 50 plus taking 3 common from this we can see 3 is common in all the terms so taking 3 common 3 multiplied by 1 plus 2 plus 3 so on till 9 which is equal to 2 multiplied by 50 plus 3 multiplied by this is the sum of n terms so which is equal to n by 2 multiplied by a plus l where n is the number of terms a is the first term and l is the last term which is equal to 2 multiplied by 50 plus 3 multiplied by n is equal to 9 so 9 by 2 multiplied by a is equal to 1 plus l is equal to that is last term again 9 which is equal to 2 multiplied by 50 plus 3 multiplied by 9 by 2 multiplied by 1 plus 9 is equal to 10 which is equal to 2 multiplied by 50 plus 3 multiplied by this 10 gets cut off with 2 and we get here 5 so 9 multiplied by 5 is equal to 45 which is equal to 2 multiplied by 50 plus 3 multiplied by 45 is equal to 135 which is equal to 2 multiplied by 50 plus 135 is equal to 185 which is equal to 370 hence total distance covered by the competitor is equal to 370 meter I hope you understood the question bye and have a nice day