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- 1.3 Geometric sequences and series.
- 1.4 Financial applications of geometric sequences and series.
- 1.8 Sum of infinite convergent geometric sequences

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Interest Practise using the formulas for simple interest and compound interest.
- Interest Video Learn about simple interest, compound interest, appreciation and depreciation. This video is to help you do the online, self-marking exercise.
- Geometric Sequences An exercise on geometric sequences including finding the nth term and the sum of any number of terms.
- Compound Interest Calculator A customised online calculator for quickly finding the solutions to compound interest problems.
- Parts of Sequences Find the formula that describes the part of the sequence that can be seen
- Sigma Practise using the sigma notation to find the sum of various number series.

Here are some exam-style questions on this topic:

- "
*Elaine invests £150 000 in a savings account for six years.*" ... more - "
*Winky Lash wants to invest £20 000 for 3 years in a bank. She has the following two choices of banks, both offering compound interest but on different terms:*" ... more - "
*The value of a boat is £220 000.*" ... more - "
*The value of a new car is £22 000.*" ... more - "
*Michael Banks invests £2000 in a savings account for two years. The account pays 2% compound interest per annum.*" ... more - "
*The value of a new house, \(V\), is given by:*" ... more - "
*Here are the details for two bank accounts.*" ... more - "
*Montague invests £7000 for six years in a bank offering compound interest at \(x%\) per annum.*" ... more - "
*On Billy's 16th birthday his parents gave him options of how he might receive his monthly allowance for the next two years.*" ... more - "
*The diagrams above show a growing fractal of triangles. The sides of the largest equilateral triangle in each diagram are of length 1 metre.*" ... more - "
*A square is drawn with sides of length 32 cm. The midpoints of the sides of this square are joined to form a new square and four red triangles. The process is repeated to produce yellow triangles and then again to produce blue triangles.*" ... more - "
*All answers to this question should be given to the nearest whole currency unit.*" ... more - "
*Two friends Arthur and Babette, each set themselves a target of saving £12000. They each have £6800 to invest.*" ... more - "
*The first term of an infinite geometric sequence is 10. The sum of the infinite sequence is 500.*" ... more - "
*In a geometric series the common ratio is \(r\) and sum to \(n\) terms is \(S_n\).*" ... more - "
*Chris checks his Twitter account and notices that he received a tweet at 8:00am. At 8:05am he forwards the tweet to four people. Five minutes later, those four people each forward the tweet to four new people. Assume this pattern continues and each time the tweet is sent to people who have not received it before.*" ... more - "
*Ruby invests a certain amount of money in a bank account that pays a nominal annual interest rate of 6.7%, compounded quarterly.*" ... more - "
*(a) Expand the following as the sum of six terms:*" ... more - "
*Consider the number sequence where \(u_1=500, u_2=519, u_3=538\) and \(u_4=557\) etc.*" ... more

Here are some Advanced Starters on this statement:

**Grandmother**

How far would grandma have travelled after a suitably large number of days given her walking regime? more**Rice on a Chess Board**

How many grains of rice are on a chess board if each square has twice the number of grains as the previous square. more**Same Series Sum**

Find an arithmetic series and a geometric series that have the same sum of the first five terms. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Money For many pupils the ability to understand financial transactions is a skill they thank their mathematics teacher for. Understanding the use of money is a real, practical application of mathematics in the real world and is just as important today as ever it was. When it comes to managing our money and avoiding costly mistakes it is well worthwhile to strive to become an expert. There are key aspects of personal finance the pupils should understand as the get older and more independent in their lives and the activities provided here provide resources for a small part of their learning process.
- Sequences A pattern of numbers following a rule is called a sequence. There are many different types of sequence and this topic introduces pupils to some of them. The most basic sequences of numbers is formed by adding a constant to a term to get the next term of the sequence. This rule can be expressed as a linear equation and the terms of the sequence when plotted as a series of coordinates forms a straight line. More complex sequences are investigated where the rule is not a linear function. Other well-known sequences includes the Fibonacci sequence where the rule for obtaining the next term depends on the previous two terms. Sequences can be derived from shapes and patterns. A growing patterns of squares or triangles formed from toothpicks is often used to show linear sequences in a very practical way. Diagrams representing sequences provides interesting display material for the classroom. Typically pupils are challenged to find the next term of a given sequence but a deeper understanding is needed to find intermediate terms, 100th term or the nth term of a sequence.

This Scheme of Learning was produced by White Rose Maths and is used here with permission granted on 30th June 2021.