In a potato race 20 potato are placed in a line at intervals of 4 meters with the first potato 24 meters from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes? [NCERT EXEMPLAR]
Given: total potatoes are 20. First potato is 24 meters away from starting point equal distance between two adjacent potatoes is 4 meters
To find: the total distance run by contestant
As contestant is coming back to starting point after bringing every potato
Distance covered by him to bring 1st potato and return to the initial position is 24m + 24m = 48m
Now, distance between adjacent trees is 4m
Distance covered by him to bring 2nd potato and return to the initial position is 28m + 28m = 56m
Distance covered by him to bring 3rd potato return to the initial postion is 32m + 32m = 64m
Hence distance covered by him to bring the potatoes are in A.P
A.P. is 48, 56, 64………………………………………upto 20 terms
Here first term, a = 48, common difference, d = 56 – 48 = 8
And n = 20
We need to find S20 which will be the total distance covered by contestant to bring 20 potatoes
Formula used:
where a is first term, d is common difference and n is number of terms in an A.P.
Therefore,
⇒ S20 = 2480
Hence, total distance covered by contestant to bring potatoes is 2480 m