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Aron is training for a 10 km marathon swim in 19 weeks. Each week, his training plan includes a long distance swim. In week six, Aron swam a total of 18.75 km. In week ten, Aron swam a total of 36.25 km. Each week, Aron increased the distance he swam following an arithmetic sequence until the final week. In the last week, Aron only swam 5 km in order to save energy for the race.

a. By what distance did Aron increase his total swimming each week?



b. Determine the distance Aron swam in the first week of training.

c. Determine how far Aron swam in the 18-week training program

To answer the questions related to Aron's training for the 10 km marathon swim, we need to use the information provided and solve some arithmetic problems. Let's break down each question and figure out how to find the answers.

a. By what distance did Aron increase his total swimming each week?

To find the increase in distance each week, we need to calculate the difference between the total distances swam in consecutive weeks. In this case, we can subtract the total distance swam in week six from the total distance swam in week ten:

(Week 10 distance) - (Week 6 distance) = 36.25 km - 18.75 km = 17.5 km

Therefore, Aron increased his total swimming distance by 17.5 km each week.

b. Determine the distance Aron swam in the first week of training.

To find the distance Aron swam in the first week of training, we need to find the starting point of the arithmetic sequence. We know that Aron swam 18.75 km in week six, so we can subtract five times the increase in distance (17.5 km) from this value:

(Week 6 distance) - (5 * increase) = 18.75 km - (5 * 17.5 km) = 18.75 km - 87.5 km = -68.75 km

Since distance cannot be negative, it seems there may be an error in the given information or calculation. Please double-check the question or the values provided.

c. Determine how far Aron swam in the 18-week training program

To find the total distance Aron swam in the 18-week training program, we need to calculate the sum of the distances swam each week. We know that Aron swam 5 km in the last week and increased his distance by 17.5 km each week.

Using the arithmetic sum formula, we can calculate the sum:

Sum = (n/2) * (first term + last term)
where n is the number of terms (weeks).

In this case, n = 18, the first term is what we need to find, and the last term is 5 km.

Sum = (18/2) * (first term + 5 km)
Sum = 9 * (first term + 5 km)

Now, we also know that the sum is equal to the total distance swam in the program, which is what we want to find. Let's use a variable, D, to represent the total distance.

D = 9 * (first term + 5 km)

Therefore, we cannot find the total distance swam in the 18-week training program without knowing the value of the first term or having more information.

a. (36.25-18.75)/4 = ?

b. 18.75 - ?/10 = ??

I'll leave the rest to you.