Question

3. John has €500, and wants to go on a holiday, but does not have sufficient money. He decides to save €40 per week for a number of weeks to make up the deficit.

a. Given that he has €500 at the beginning of the first week, how much will he have saved at the end of the, 2nd, 3rd, 4th and 5th weeks?

Answer 1

John will have saved 540 by the 2nd week, 580 by the third week, 620 by the fourth week and 660 by the fith week.

Explanation:

The amount of money John saves as the weeks go on can be modelled by a arithmetic sequence where the first term is 500 and the ratio is 40. Therefore the amount of money saved by week is given by:

an = a0 + (n-1)*r

In this case a0 = 500 and r = 40. We have:

an = 500 + (n-1)*40

So, for the second week:

a2 = 500 + (2 - 1)*40 = 500 + 40 = 540

For the third week:

a3 = 500 + (3 - 1)*40 = 500 + 2*40 = 580

For the fourth week:

a4 = 500 + (4-1)*40 = 500 + 3*40 = 620

For the fith week:

a5 = 500 + (5-1)*40 = 500 + 4*40 = 660