# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#10

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**Question**

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.

She will then increase 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,

**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.

**Solution**

**a.
**

From the given information we can collect following data.

It is evident that numbers of minutes each day run by Xin form an arithmetic sequence.

We are required to calculate the number of minutes run on day fourteen.

It is evident that we are looking for 14^{th }term of said arithmetic sequence.

Expression for the general term in the Arithmetic Progression (A.P) is:

Therefore;

**b.
**

From the given information we can collect following data.

We are given that Yi and Xin will run for the same length of time on day 14.

We have already calculated running time of Xin on day fourteen in (a), it is evident that we are looking for running time of Yi on day fourteen.

It is evident that we are looking 14^{th} term of said arithmetic sequence.

Expression for the general term in the Arithmetic Progression (A.P) is:

Therefore;

Since time run by both on day fourteen is equal;

**c.
**

We are given Xin runs for a total time of 784 minutes over the 14 days.

It is evident that some of 14 terms of following arithmetic sequence, found in (a), is 784.

Expression for the sum of number of terms in the Arithmetic Progression (A.P) is:

Therefore;

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