Respuesta :
Answer:
I believe the answer is D) 26.
Step-by-step explanation:
Xavier will need 26 weeks to first bike more than 500 miles.
Arithmetic Progression
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the successive terms is the same.
Sum of n terms of an arithmetic progression
The distance biked by Xavier during his first week of training is 15 miles.
The increase in the distance biked each week is 0.4 miles.
And we have to find the number of weeks required to first bike more than 500 miles total.
The given situation represents an arithmetic progression (AP) in which,
First term, a = 15
The common difference, d = 0.4
And the sum of n terms, Sn = 500
The formula to find the sum of n terms of an AP is,
[tex]\text{S}_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
How to check which option is correct?
We will check which option is correct by putting them in the above equation.
For n = 8, we have
[tex]\text{S}_n = \dfrac{8}{2}[2\times15+(8-1)0.4][/tex]
Sn = 4[30+2.8]
Sn = 131.2
Which is not more than 500, so option (A) is incorrect.
For n = 15, we have
[tex]\text{S}_n = \dfrac{15}{2}[2\times15+(15-1)0.4][/tex]
Sn = 7.5[30+5.6]
Sn = 267
Which is not more than 500, so option (B) is incorrect.
For n = 19, we have
[tex]\text{S}_n = \dfrac{19}{2}[2\times15+(19-1)0.4][/tex]
Sn = 9.5[30+7.2]
Sn = 353.4
Which is not more than 500, so option (C) is incorrect.
For n = 26, we have
[tex]\text{S}_n = \dfrac{26}{2}[2\times15+(26-1)0.4][/tex]
Sn = 13[30+10]
Sn = 520
Which is more than 500, so option (D) is the correct answer.
Hence, Xavier would bike more than 500 miles in 26 weeks.
Learn more about arithmetic progression here - https://brainly.com/question/27029595
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