**CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.3 Question 20**

**20. In a potato race, a bucket is placed at the starting point, which is 5 meters from the first potato, and the other potatoes are placed 3 meters apart in a straight line. There are ten potatoes in the line. 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?**

**Solution:**

The distance of first potato from the starting point = 5 meters

Therefore, the distance covered by competitor to pickup first potato and put it in bucket = 5 x 2 = 10 meters

The distance of Second potato from the starting point = 5 + 3 = 8 meters {All the potatoes are 3 meters apart from each other}

Therefore, the distance covered by competitor to pickup 2nd potato and put it in bucket = 8 x 2 = 16 meters

The distance of third potato from the starting point = 8 + 3 = 11 meters

Therefore, the distance covered by competitor to pickup 3rd potato and put it in bucket = 11 x 2 = 22 meters

**Therefore, we have a sequence of the form 10, 16, 22, ....10 terms (There are ten terms because there are ten potatoes)**

To calculate the total distance covered by the competitor, we need to find :

**10 + 16 + 22 + .... 10 terms**

First term = a = 10

Common difference = d =16 - 10 = 6

n = 10 {There are total of 10 terms in the sequence}

**Applying formula**, to find sum of n terms of AP , **we get**

**Therefore, total distance covered by competitor is equal to 370 meters.**