# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#4

Question

A company, which is making 140 bicycles each week, plans to increase its production.

The number of bicycles produced is to be increased by d each week, starting from 140

in week 1, to 140 + d in week 2, to 140 + 2d in week 3 and so on, until the company is producing  206 in week 12.

a.   Find the value of d.

After week 12 the company plans to continue making 206 bicycles each week.

b.   Find the total number of bicycles that would be made in the first 52 weeks starting from and  including week 1.

Solution

a.

From the given information we can collect following data;

It is evident that number of bicycles produced  each week form an arithmetic sequence.

We are also given that company produces 206 in week 12.

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

Therefore;

b.

We are required to calculate the total number of bicycles produced in first 52 weeks.

It is evident that number of bicycles produced from 1 to 12 weeks form an arithmetic sequence and  then continues to produce 206 bicycles weekly from 13 to 52 week.

First we find total number of bicycles produced in weeks 1 to 12.

It is evident that we are looking for sum of first 12 terms of said arithmetic sequence.

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

Therefore;

Afterwards company continues to produce 206 bicycles weekly from 13 to 52 week (for 40 weeks).

Hence, total number of bicycles produced in 52 weeks is;