Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#9

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Question

Jess started work 20 years ago. In year 1 her annual salary was £17000. Her annual salary  increased by £1500 each year, so that her annual salary in year 2 was £18500, in year 3 it was  £20000 and so on, forming an arithmetic sequence. This continued until she reached her maximum  annual salary of £32000 in year k. Her annual salary then remained at £32000.

a.   Find the value of the constant k.

b.   Calculate the total amount that Jess has earned in the 20 years.

Solution

a.
 

It is given that the salaries received by Jess form an arithmetic sequence.

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

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

Therefore;

We are required to show that salary for  9th year will be £26 000.

We are given that her maximum annual salary of £32000 in year k. Her annual salary then  remained the same.

We are required to find the constant k.

It is evident that we are looking for number of the term which is 32000 in given arithmetic sequence

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

Therefore;

b.
 

We are required to find the total amount earned during 20 years of job by Jess.

It is evident that we are looking for the sum of 11 terms of above given arithmetic sequence and 9  years of fixed salary.

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

Therefore;

We are given that salary remained same for next 9 years at £32000.

Hence, his total earning during 20 years will be;

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