New
New
Problem solving with further sequences
I can use my enhanced knowledge of sequences to solve problems.
Lesson 9 of 9
New
New
- Year 11
Problem solving with further sequences
I can use my enhanced knowledge of sequences to solve problems.
Lesson details
Key learning points
- Compound interest can be thought of as a geometric sequence.
- You can apply your knowledge of geometric sequences to solve compound interest problems.
Keywords
Interest - Interest is money added to savings or loans.
Compound interest - Compound interest is calculated on the original amount and the interest accumulated over the previous period.
Geometric sequence - A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.
Common ratio - In a geometric sequence, the constant multiplier between successive terms is called the common ratio.
Common misconception
A multiplier of 1.3 is used to increase a value by 3%
A multiplier of 1.3 is used to increase a value by 30%
The final question in Task B has a large version of Pascal's triangle on the final page of the worksheet. This could be printed and laminated to allow pupils to investigate shading the triangle without each pupil needing multiple copies of the triangle.
Teacher tip
Licence
This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Interest which is calculated on the original amount and the interest accumulated over the previous period is called __________ interest.
Interest which is calculated on the original amount and the interest accumulated over the previous period is called __________ interest.
average
linear
repeated
simple
Q2.Match the type of sequence with its description.
Match the type of sequence with its description.
Q3.Which of these could be the first 5 terms in an arithmetic sequence?
Which of these could be the first 5 terms in an arithmetic sequence?
1, 2, 4, 8, 16, ...
15, 18, 22, 24, ...
16, 40, 100, 250, 375, ...
Q4.Which of these could be the first 5 terms in a geometric sequence?
Which of these could be the first 5 terms in a geometric sequence?
1, 4, 16, 36, 64, ...
3, 5, 8, 12, 20, ...
5, 10, 15, 20, 25, ...
Q5.If a geometric sequence starts 20, 60, 180, ... what is the common ratio (common multiplier)?
If a geometric sequence starts 20, 60, 180, ... what is the common ratio (common multiplier)?
Q6.If a geometric sequence starts 50, 60, 72, ... what is the common ratio? Give your answer as a decimal.
If a geometric sequence starts 50, 60, 72, ... what is the common ratio? Give your answer as a decimal.
Assessment exit quiz
6 Questions
Q1.What type of sequence has been shaded on Pascal's triangle?
What type of sequence has been shaded on Pascal's triangle?
An alternating sequence
A Fibonacci sequence
A geometric sequence
A quadratic sequence (sequence with common second difference)
Q2.Which of these best describes the sequence of numbers shaded on Pascal's triangle?
Which of these best describes the sequence of numbers shaded on Pascal's triangle?
An arithmetic sequence
A geometric sequence
The sequence of all cube numbers
The sequence of all square numbers
Q3.£24 000 is borrowed at a compound interest rate of 5% a month. How much is owed after 3 months?
£24 000 is borrowed at a compound interest rate of 5% a month. How much is owed after 3 months?
Q4.£800 is borrowed with yearly compound interest and after a year £1040 is owed. What is the yearly interest rate?
£800 is borrowed with yearly compound interest and after a year £1040 is owed. What is the yearly interest rate?
1.3%
13%
25%
40%
Q5.A loans company charges 6% interest a month. If £2650 was owed after one month, how much was borrowed?
A loans company charges 6% interest a month. If £2650 was owed after one month, how much was borrowed?
Q6.£750 was borrowed with compound interest and after 2 years making no repayments £1080 was owed. What was the yearly interest rate?
£750 was borrowed with compound interest and after 2 years making no repayments £1080 was owed. What was the yearly interest rate?
6.6%
18%
44%
72%
