Arithmetic series

Question

Arithmetic Series question

1. Xin has been given a 14 day training schedule by her coach.

Xin will run A minutes on day 1, where A is constant.

She will then increases her running time (d+1) minutes each day, where d is constant.

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

Yi has also been given a 14day training schedule by her coach.

Yi will run (A-13) minutes on day 1.

She will then increases her running time by (2d - 1) minutes each day. Given that Yi and Xin will run for the same length of time on day 14.

Question b) Calculate the value of d

Given that Xin run for a total time of 784 minutes over the 14 days.

Question C) Find the value of A

Answer 1

Arithmetic series have the following form: S_n = S₁ + (n - 1)D where

 

S₁: the starting value

 

D: the difference between successive terms

 

 

Xin:

 

On the 14th day, n - 1 = 14 -1 = 13 and D = d + 1

 

S₁₄ = A + 13(d + 1) for the number of minutes Xin runs on the 14th day.

 

 

Yi:

 

On the 14th day, S₁ = A - 13 and D = 2d - 1

 

S₁₄ = (A - 13) + 13(2d - 1) = A - 13 + 26d - 13 = A + 26d - 26

 

 

A + 13d + 13 = A + 26d - 26

 

13d = 39

 

d = 3

 

784 = A + 13(3) + 1

 

A = 744