Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#8

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Question

In the year 2000 a shop sold 150 computers. Each year the shop sold 10 more computers than the  year before, so that the shop sold 160 computers in 2001, 170 computers in 2002, and so on  forming an arithmetic sequence.

a.   Show that the shop sold 220 computers in 2007.

b.   Calculate the total number of computers the shop sold from 2000 to 2013 inclusive.

In the year 2000, the selling price of each computer was £900. The selling price fell by £20 each  year, so that in 2001 the selling price was £880, in 2002 the selling price was £860, and so on  forming an arithmetic sequence.

c.   In a particular year, the selling price of each computer in £s was equal to three times the number  of computers the shop sold in that year. By forming and solving an equation, find the year in which  this occurred.

Solution

a.
 

We are given that number of computers sold each year form an arithmetic sequence.

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

We are required to find number of computers sold in 2007.

It is evident that we are looking for 8th term of said arithmetic sequence.

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

Therefore;

b.
 

We are required to calculate the total number of computers the shop sold from 2000 to 2013  inclusive.

It is evident that we are looking for sum of first 14 terms of said arithmetic sequence.

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

Therefore;

c.
 

We are given that selling prices of computer from 2000 onwards form an arithmetic sequence. 

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

We are given that in a particular year, the selling price of each computer was equal to three times  the number of computers the shop sold in that year.

We can write it mathematically as;

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

Therefore;

Hence, the selling price of each computer was equal to three times the number of computers the  shop sold in 2009 year.

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