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

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): You can put this solution on YOUR website!
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
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