Interest is money added to savings or loans.

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

A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.

In a geometric sequence, the constant multiplier between successive terms is called the common ratio.

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

Checking and securing understanding of geometric sequences

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

A quadratic sequence (sequence with common second difference)

What type of sequence has been shaded on Pascal's triangle?

Which of these best describes the sequence of numbers shaded on Pascal's triangle?

£24 000 is borrowed at a compound interest rate of 5% a month. How much is owed after 3 months? 

£800 is borrowed with yearly compound interest and after a year £1040 is owed. What is the yearly interest rate?

A loans company charges 6% interest a month. If £2650 was owed after one month, how much was borrowed?

£750 was borrowed with compound interest and after 2 years making no repayments £1080 was owed. What was the yearly interest rate?

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

a sequence with a common difference between successive terms.

a sequence where each term is the sum of the two previous terms.

a sequence with a common multiplier between successive terms.

a sequence with a common second difference.

Match the type of sequence with its description.

Which of these could be the first 5 terms in an arithmetic sequence?

Which of these could be the first 5 terms in a geometric sequence?

If a geometric sequence starts 20, 60, 180, ... what is the common ratio (common multiplier)?

If a geometric sequence starts 50, 60, 72, ... what is the common ratio? Give your answer as a decimal.

Problem solving with further sequences

Lesson outcome