What is the distance covered to pick up the 7?? potato?

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Solution

Q.
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato.
The other potatoes are arranged 3 m apart in a straight line, with a total of ten potatoes, as shown in the figure.

A competitor starts from the bucket, picks up the nearest potato, runs back to the bucket to drop it in, then returns to pick up the next potato.
This process continues until all the potatoes are in the bucket

Based on the above information answer the following questions:

(i) What is the distance covered to pick up the 7th potato

1 46 m

2 44 m

3 45 m

4 41 m

Ans.
(1)

Distance covered to pick up the 1st potato =2(5 m) = 10 m

Distance between two successive potatoes = 3 m

Distance covered to pick up the 2nd potato =2(5+3)=16 m

Distance covered to pick up the 3rd potato =2(5+3+3)=22 m

So the distances are: 10, 16, 22, …

This forms an AP where: $a = a_{1} = 10, a_{2} = 16, d = 16 - 10 = 6$

Distance covered to pick up 7?? potato $= 2 (5 + 6 \times 3) = 2 \times 23 = 46 m$

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