Sequences and series in modellingEdexcel A-Level Maths: Subtopic test

1. 1
   Aisha saves money each month. In month 1 she saves £50, and in each later month she saves £8 more than in the previous month.

   (a)

   How much does Aisha save in month 12?

   [1 mark]

   • A£138
   • B£146
   • C£88
   • D£96

   (b)

   How much does Aisha save altogether in the first 12 months?

   [1 mark]

   • A£1,656
   • B£1,128
   • C£564
   • D£1,176

   (c)

   Find the first month in which Aisha saves more than £300.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A tree is 1.20 m tall when planted. It grows 0.50 m in the first year, and in each later year its growth is 85% of its growth in the previous year.

   (a)

   How much does the tree grow in year 3?

   [1 mark]

   • A0.425 m
   • B0.307 m
   • C0.361 m
   • D0.011 m

   (b)

   According to this model, what height does the tree approach in the long run?

   [1 mark]

   • A3.33 m
   • B1.79 m
   • CThere is no greatest height, because the tree grows every year.
   • D4.53 m

   (c)

   Find the height of the tree after 5 years.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   At the start of each year Ben pays £1500 into a savings account that pays 3% compound interest, added at the end of each year. The first payment is at the start of year 1 and no money is withdrawn.

   (a)

   Show that the amount in the account at the end of year 3 is £4775.44.

   [3 marks]

   (b)

   Find the amount in the account at the end of year 10.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two savings plans are compared. Plan A: £100 is paid in month 1, and each later monthly payment is £12 more than the one before. Plan B: £100 is paid in month 1, and each later monthly payment is 8% more than the one before.

   (a)

   For plan A, find:
   (i) the total paid in the first 24 months,
   (ii) the first month in which the monthly payment exceeds £500.

   [6 marks]

   (b)

   For plan B:
   (i) show that the total paid in the first 24 months is £6676 to the nearest pound,
   (ii) find the first month in which the monthly payment under plan B exceeds that under plan A,
   (iii) state which plan has the larger total after 24 months and by how much, to the nearest pound.

   [6 marks]

   Total for question 4: 12 marks

End of questions