Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | June | Q#4

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Question

A girl saves money over a period of 200 weeks. She saves 5p in Week 1, 7p in Week 2, 9p in Week  3, and so on until Week 200. Her weekly savings form an arithmetic sequence. 

a.   Find the amount she saves in Week 200.

b.   Calculate her total savings over the complete 200 week period.

Solution

a.
 

We are given that the 200 savings of girl form an arithmetic sequence with following data;

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

Therefore;

 

We are required to find the savings made on 200th week.

It is evident that we are looking for 200th term of above given arithmetic sequence.

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

Therefore;

Hence, she saved 403p on 200th week.

b.
 

We are required to find total savings on 200 weeks by the girl.

It is evident that we are looking for the sum of 200 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 saving over 200 weeks is 40800p.

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