Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#7

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Question

A company, which is making 200 mobile phones each week, plans to increase its production. The  number of mobile phones produced is to be increased by 20 each week from 200 in week 1 to 220 in week 2, to 240 in week 3 and so on, until it is producing 600 in week N.

a.   Find the value of N.

The company then plans to continue to make 600 mobile phones each week.

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

Solution

a.
 

We can see that number of mobile phones produced in each week form an arithmetic sequence.

From the given information we can collect following data about the said arithmetic sequence.

We are required to find N.

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

Therefore;

b.
 

As demonstrated in (a), first time 600 mobiles are produced in 21st week and then company, we are  given, continues to produce 600 mobile phones per week till 52nd week.

Hence, total number of mobile phones produced in 52 weeks consists of sum of first 20 weeks (in  arithmetic sequence) and then 600 in each week for the next 22 weeks.

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

Therefore;

Hence, his total mobile phones produced in first 20 weeks are 7800.

Hence, total number of mobile phones produced by company in 52 weeks;

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