# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#7

Question

Each year, Abbie pays into a saving scheme. In the first year she pays in £500. Her payments the  increase by £200 each year so that she pays £700 in the second year, £900 in the third year and so  on.

a.   Find out how much Abbie pays into the saving scheme in the tenth year.

Abbie pays into the scheme for n years until she has paid in a total of £67200.

b.   Show that

c.   Hence find the number of years that Abbie pays into the saving scheme.

Solution

a.

We can see that hear yearly payments form an arithmetic sequence.

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

We are required to find the amount of payment made in 10th year.

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

Therefore;

She paid £2300 into the saving scheme in 10th year.

b.

Abbie paid a total amount of £67200 in n years.

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

Therefore;

c.

We are required to find the total number of years ie n.

From (b) we have;

Now we have two options.

Since total number of years cannot be negative;