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Aron is training for a 10 km marathon swim in 18 weeks. Each week, his training plan
includes a long distance swim. Over the first 6 weeks, Aron swam a total of 18.75 km. Over
the first 10 weeks, Aron swam a total of 36.25 km. Each week, Aron increased the distance
he swam following an arithmetic sequence until the final week.
a. By what distance did Aron increase his total swimming each week?

Respuesta :

mathstudent55

Answer:

a. 0.25 km

Step-by-step explanation:

For an arithmetic sequence, the sum of all terms up to term n is

sum = n/2[2a + (n - 1)d]

We are given:

sum of first 6 terms = 18.75

sum of the first 10 terms = 36.25

6/2[2a + (6 - 1)d] = 18.75

10/2[2a + (10 - 1)d] = 36.25

3(2a + 5d) = 18.75

5(2a + 9d) = 36.25

2a + 5d = 6.25

2a + 9d = 7.25

4d = 1

d = 0.25

2a + 5(0.25) = 6.25

2a = 5

a = 2.5

The common difference is 0.25 km.

Answer: a. 0.25 km

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