Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | January | Q#7

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Question

Jill gave money to a charity over a 20-year period, from Year 1 to Year 20 inclusive. She gave £150  in Year 1, £160 in Year 2, £170 in Year 3, and so on, so that the amounts of money she gave each  year formed an arithmetic sequence.

a.   Find the amount of money she gave in Year 10.

b.   Calculate the total amount of money she gave over the 20-year period.

Kevin also gave money to the charity over the same 20-year period. He gave £A in Year 1 and the  amounts of money he gave each year increased, forming an arithmetic sequence with common  difference £30. 

The total amount of money that Kevin gave over the 20-year period was twice the total amount of money that Jill gave.

c.   Calculate the value of A.

Solution

a.
 

We are given that the amounts of money Jill gave each year form an arithmetic sequence. 

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

Jill gave money to a charity over a 20-year period, from Year 1 to Year 20 inclusive.

She gave £150 in Year 1, £160 in Year 2, £170 in Year 3.

Expression for difference  in Arithmetic Progression (A.P) is:

Therefore;

We are required to find the amount of money she gave in Year 10.

It is evident that we are looking for 10th term of above given arithmetic sequence.

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

Therefore;

Hence, she saved 240£ on 10th year.

b.
 

We are required to find the total amount of money Jill gave over the 20-year period.

It is evident that we are looking for the sum of 20 terms of above given arithmetic sequence.

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

Therefore;

Hence, her total charity over 20 years is 4900p.

c.
 

We are given that the amounts of money Kevin gave each year form an arithmetic sequence. 

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

He gave £A in Year 1 and the amounts of money he gave each year increased, forming an  arithmetic sequence with common difference £30.

The total amount of money that Kevin gave over the 20-year period was twice the total amount of  money that Jill gave.

We are required to find A that is the first term.

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

Therefore;

Hence, his charity on year 1 is 205£.

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