Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#6

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Question

A boy saves some money over a period of 60 weeks. He saves 10p in week 1, 15p in week 2, 20p  in week 3 and so on until week 60. His weekly savings form an arithmetic sequence. 

a.   Find how much he saves in week 15

b.   Calculate the total amount he saves over the 60 week period. 

The boy’s sister also saves some money each week over a period of m weeks. She saves 10p in week 1, 20p in week 2, 30p in week 3 and so on so that her weekly savings form an arithmetic  sequence. She saves a total of £63 in the m weeks.

c.   Show that

d.   Hence write down the value of m.

Solution

a.
 

We are given that the amounts of money boy saves gave each week form an arithmetic sequence. 

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

Boy saves money over a 60-week period, from Week 1 to Wee 60 inclusive.

He gave 10p in Week 1, 15p in Week 2, 20p in Week 3.

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

Therefore;

We are required to find the amount of money he saved in Week 15.

It is evident that we are looking for 15th term of above given arithmetic sequence.

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

Therefore;

Hence, he saved 80p on 15th week.

b.
 

We are required to find the total amount of money he saves over the 60-week period.

It is evident that we are looking for the sum of 60 terms of above given arithmetic sequence.

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

Therefore;

Hence, his total saving over 60 weeks is 9450p.

c.
 

We are given that the amounts of money girl saves each week form an arithmetic sequence.

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

Girl saves money over a m-week period, from Week 1 to Wee m inclusive.

She saves 10p in Week 1, 20p in Week 2, 30p in Week 3.

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

Therefore;

She saves a total of £63 (6300p) in the m weeks.

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

Therefore;

d.
 

Now we have two options.

Since  represents total number of weeks for which the girl have been saving, therefore, it cannot be negative. Hence;

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