Interest is money added to savings or loans.

Compound interest is calculated on the original amount and the interest accumulated over the previous period.

The general form for an exponential equation is y = ab^x where a is the coefficient, b is the base and x is the exponent.

Advanced problem solving with further sequences

Maths

Checking and securing understanding of special number sequences

Fibonacci and alternating sequences

Checking and securing rules for generating arithmetic sequences

Identifying values in an arithmetic sequence

Reasoning about values in an arithmetic sequence

Conditions in arithmetic sequences

Arithmetic sequences and their graphs

Introducing quadratic sequences

Quadratic sequences

Checking and securing understanding of geometric sequences

Sequence notation

In the prior unit, pupils considered other types of graphs. In this unit, pupils consider different types of sequences such as Fibonacci and oscillating. Their knowledge is consolidated by linking all prior learning together.

In this unit, pupils consider different types of sequences such as Fibonacci and oscillating sequences. They then consolidate their knowledge of different types of sequences by solving contextual problems.

Further sequences

£1600 is borrowed with yearly compound interest and after a year £2240 is owed. What is the yearly interest rate?

A loans company charges 4% interest a month. If £35 152 was owed after three months, how much was borrowed?

£40 000 was borrowed with compound interest and after 4 years £58 564 was owed. What was the yearly interest rate? Assume no repayments were made.

£24 000 is borrowed at a compound interest rate of 5% a month. What would be the $$n^\text{th}$$ term rule for the geometric sequence formed from the amount owed each month starting with month 1?

Some money was borrowed with compound interest. After 2 years £4000 was owed and after 4 years £6250 was owed. After how many years would the loan value be greater than £10 000 ?

$$\frac{1}{2}n^2 -\frac{1}{2}n + \frac{1}{2}$$

Which of these is the $$n^\text{th}$$ term rule for the triangular numbers? (1, 3, 6, 10, 15, ...)

Interest which is calculated on the original amount and the interest accumulated over the previous period is called {{}} interest.

If a geometric sequence starts 75, 105, 147, ... what is the common ratio? Give your answer as a decimal.

£100 is invested at 1% compound interest a month. Which calculation would find the value of the money after 5 months?

Which of these are examples of exponential equations? 

Which of these is the general form for an odd number when $$n$$ is an integer?

What is the $$n^\text{th}$$ term of the quadratic sequence which starts 1, 3, 9, 19, 33, ...?

Advanced problem solving with further sequences

Lesson outcome