Respuesta :
Answer:
[tex]a_n = 3n[/tex]
Step-by-step explanation:
Each week Shelly rides her bicycle 3 miles farther than the week before.
In the 1st week she rides 3 miles.
In the 2nd week she rides 3 + 3 = 6 miles
In the 3rd week she rides 6 + 3 = 9 miles
In the 4th week she rides 9 + 3 = 12 miles
In the 5th week she rides 12 + 3 = 15 miles
So we have sequence of 3, 6, 9, 12, 15,....
The general form to represent an arithmetic sequence is given by
[tex]a_n = a_1 + (n - 1)\cdot d[/tex]
Where [tex]a_n[/tex] is the nth term, [tex]a_1[/tex] is the first term and [tex]d[/tex] is the common difference.
The common difference is the difference between any two consecutive terms.
In this case we have
[tex]a_1 = 3\\\\d = 6-3 = 3[/tex]
So the above equation becomes
[tex]a_n = a_1 + (n - 1)\cdot d\\\\a_n = 3 + (n - 1)\cdot 3\\\\a_n = 3 + 3n - 3\\\\a_n = 3n[/tex]
So this the the required rule that relates the number of weeks (n) Shelly has been training to the numbers of miles she rides.
For example:
To find out how many miles Shelly will ride in the 10th week,
[tex]a_n = 3n\\\\a_{10} = 3(10)\\\\a_{10} = 30\: miles\\\\[/tex]
To write in terms of fractions in simplest form
[tex]\frac{week}{miles} = \frac{10}{30} = \frac{1}{3}[/tex]
Answer:
Step-by-step explanation:
The rule that relates the number if weeks Shelly has been training to the number of miles she rides is determined by multiplying the training weeks by 3.
Training weeks 1 2 3 4 5 6
Riding (miles) 3
If for the first training weeks; she rode her bicycle for 3 miles
Then for the second training weeks ; her riding miles will be 2 × 3 = 6 miles ( going by the rule described above )
Third week = 3 × 3 = 9 miles
Fourth week = 4 × 3 = 12 miles
Fifth week = 5 × 3 = 15 miles
Sixth week = 6 × 3 = 18 miles
Training weeks 1 2 3 4 5 6
Riding (miles) 3 6 9 12 15 18
The fractions are:
[tex]\frac{1}{3} ; \ \ \frac{2}{6} ; \ \ \frac{3}{9} ; \ \ \frac{4}{12} ; \ \ \frac{5}{15} ; \ \ \frac{6}{18}[/tex]
To simplest form; we have:
[tex]\frac{1}{3} ; \ \ \frac{1}{3} ; \ \ \frac{1}{3} ; \ \ \frac{1}{3} ; \ \ \frac{1}{3} ; \ \ \frac{1}{3}[/tex]
