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Any guidance or worked solutions would be appreciated
For a potato race, a straight line is marked on the ground from a point A, and points B,C,D,... are marked on the line so that AB = BC = CD = ... = 2 metres. A potato is placed at each of the points B,C,D,...
A runner has to start from A and bring each potato by a separate journey back to a basket at A. Find the number of potatoes so that the total distance run during the race will be 480 metres.
A) S = n/2 [2a + (n - 1) d]
B) S = n/2 [ first term + last term]
I can calculate the answer by listing out the distances covered in successive trips to obtain the required distance. However, I am unable to show relevant working and this method will not work for larger sequences.
*Tn* = 2n(n+1), where *Tn* is the 'n' th term in the sequence.
The problem is I can't find a relevant equation for the common difference, let's say, *d*.
*d* = 4(n+1) ?
I can't use equation B) as the common difference is not a constant.
Homework Statement
For a potato race, a straight line is marked on the ground from a point A, and points B,C,D,... are marked on the line so that AB = BC = CD = ... = 2 metres. A potato is placed at each of the points B,C,D,...
A runner has to start from A and bring each potato by a separate journey back to a basket at A. Find the number of potatoes so that the total distance run during the race will be 480 metres.
Homework Equations
A) S = n/2 [2a + (n - 1) d]
B) S = n/2 [ first term + last term]
The Attempt at a Solution
I can calculate the answer by listing out the distances covered in successive trips to obtain the required distance. However, I am unable to show relevant working and this method will not work for larger sequences.
*Tn* = 2n(n+1), where *Tn* is the 'n' th term in the sequence.
The problem is I can't find a relevant equation for the common difference, let's say, *d*.
*d* = 4(n+1) ?
I can't use equation B) as the common difference is not a constant.