SOLUTION: In a potato race, 10 potatoes are placed in a straight line 5 meters apart, the first potato being placed 6 meters from the starting point. how many meters does a contestant trave

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Question 1164947: In a potato race, 10 potatoes are placed in a straight line 5 meters apart, the first potato being placed 6 meters from the starting point. how many meters does a contestant travel in collecting the potatoes one at a time and placing them in a basket located at the starting point

Found 2 solutions by htmentor, Boreal:
Answer by htmentor(1343) (Show Source):
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The distance travelled to retrieve each potato will be twice the distance from the starting point to the potato.
The first distance will be 12 m since the first potato is located 6 m from the starting point
In general, the distance travelled to retrieve the n-th potato is represented by an arithmetic sequence,
with the first term equal to 12. The common difference is 10, twice the distance between each potato.
Thus a_n = 12 + 10(n-1)
The sum of 10 terms of the arithmetic sequence S_n = (10/2)*(12 + 102) = 570 m

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
It is a series with the first term 6 m out and back or 12 m
the second term is 11 m out and back or 22 m
and so forth until the n th term is (6+5(n-1)) out and back or 12+10n-10 m or 10n +2
The last term will be 102 m with n=10
so the series is 12+22+32+...+102
a1=12
a10=102
sum is (n/2)(a1+an)
=5(12+102)
=570 m
can check
12+22+32+42+52+62+72+82+92+102