MHB Athlete's Laps: Solve 1st & 6th Day + Total

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The athlete runs three more laps each day, starting with an unknown number on the first day. By the sixth day, she runs 17 laps, leading to the equation 17 = U1 + (6-1)3, resulting in U1 = 2 laps on the first day. The total laps run over six days is calculated using the formula S = (n/2)(2*U1 + (n-1)d), yielding 57 laps. However, the answer sheet states the total is 42, indicating a discrepancy, as the calculations correctly reflect the athlete's running pattern of 2, 5, 8, 11, 14, and 17 laps. The original calculations and method used are confirmed to be accurate.
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I have a Q that says:
An athlete must each day run three laps more than the day before. On the sixth day she runs 17laps
Calculate how many laps she runs 1.) on the first day 2.) in total by the end of the sixth day.

in 1.
I know that Un=U1+(n-1)d
where d=3
Un=17
n=6

i then get 17= U1 + (6-1)3, and I get U = 2

In 2 i use S=(n/2)(2*U1 + (n-1)d)
so S = (6/2)(2*2+(6-1)3) =57 (in the answer sheet it says that it's 42) what am I doing wrong?
 
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gotah said:
I have a Q that says:
An athlete must each day run three laps more than the day before. On the sixth day she runs 17laps
Calculate how many laps she runs 1.) on the first day 2.) in total by the end of the sixth day.

in 1.
I know that Un=U1+(n-1)d
where d=3
Un=17
n=6

i then get 17= U1 + (6-1)3, and I get U = 2

In 2 i use S=(n/2)(2*U1 + (n-1)d)
so S = (6/2)(2*2+(6-1)3) =57 (in the answer sheet it says that it's 42) what am I doing wrong?

Nothing, your argument has the athlete running: 2, 5, 8, 11, 14, 17. Which satisfy the conditions of the problem and sums to 57.

Also your method is correct.

CB
 
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