Arithmetic series

[Jenny]

10. Xin has been given a 14-day training schedule by her coach. Xin will run for A minutes on day 1, where A is a constant. She will then increase her running time by (d + 1) minutes each day, where d is a constant.

a) Show that on day 14, Xin will run for (A + 13d + 13) minutes.

Yi has also been given a 14-day training schedule by her coach. Yi will run for (A - 13) minutes on day 1. Given that Xin and Yi run for the same length of time on day 14,

b) find the value of d.

Given that Xin runs for a total time of 784 minutes over the 14 days,

c) find the value of A.

Really stuck on this question, would be appreciated if you could help xx

 

[stapel]

10. Xin has been given a 14-day training schedule by her coach. Xin will run for A minutes on day 1, where A is a constant. She will then increase her running time by (d + 1) minutes each day, where d is a constant.

a) Show that on day 14, Xin will run for (A + 13d + 13) minutes.

Yi has also been given a 14-day training schedule by her coach. Yi will run for (A - 13) minutes on day 1. Given that Xin and Yi run for the same length of time on day 14,

b) find the value of d.

Given that Xin runs for a total time of 784 minutes over the 14 days,

c) find the value of A.

From the subject line, you know that this has to do with arithmetic series. What have you done with that information? How far have you gotten? Where are you stuck?

Please be complete. Thank you!

 

[Jenny]

From the subject line, you know that this has to do with arithmetic series. What have you done with that information? How far have you gotten? Where are you stuck?

Please be complete. Thank you!

Hiya, i know i needed to use arithmetic series but i am very confused on how to do the questions and to start it as this question is different to the other arithmetic series questions ive done. I think its probably the letters they used xx

 

[Ishuda]

My take on the situation:

If Xin and Yi increase their run time by the same amount each day, they will never have the same run time on the same day. So What is the amount of increase in run time for Yi?

Lacking that, you can answer (a) and (c) in terms of d, i.e. the run time on day 14 is (A + 13d + 13) minutes. However (b) has no answer.

Do you know the general form for an arithmetic series? If so, write down the specific series for Xin. That will give you the answer for (a). Now, do you know the formula for the sum of a series where the terms are in arithmetic progression? Write that down and set it equal to 784 minutes and solve for A in terms of d.