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?

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.

Step-by-step 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