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GCSE foundation and higher maths students are now expected to find the nth term of a geometric sequence.

When I teach the nth term of geometric sequences I ask the class to work in pairs to categorise a range of sequences into two groups and present their solutions on mini-whiteboards. The students can decide what the categories are based on how they think the sequences are different.

I think it’s important for students to discover for themselves how a geometric sequence differs from an arithmetic sequence. Students are encouraged to use a calculator to aid their calculations. When you consider what is happening to the sequences on a term to term basis this is actually quite a simple concept and one that provokes quite a bit of class discussion.

Moving on to the development phase I introduce the common ratio by considering the term-to-term rule. For the sequence 2, 4, 8, 16, 32, 64 the common ratio is 2. This means the following term is double the previous term. We begin to generalise this on a term to term basis taking ‘a’ as the first term, a, 2a, 4a, 8a, 16a, 32a.

Now we need to find the formula for the coefficient of a. Rather than telling the class the formula I challenge them to derive it independently. The majority of the class know to raise 2 to a power. A common mistake is to raise 2 to the power of n. We discuss what this sequence would look like (2, 4, 8, 16, 32, 64) and after another minute or so most the students arrive at a × rn-1 where a is the first term of the sequence, r is the common ratio and n is the position number.

I find that once students have found the nth term for a geometric sequence they are much more likely to remember it and be able to apply it in the future.

As we work through the remaining questions the common ratio changes from an integer to a fraction. More able students are challenged to find the first term of a sequence when given two other non-consecutive terms.

In the plenary, the class are challenged to apply finding the nth term of a geometric sequence to compound percentage changes. I think it is really important students appreciate the practical, real life aspect of geometric sequences and compound interest links really nicely with this topic. I tend to allow about ten minutes for this question and have a student demonstrate the solution to their peers to feedback at the end.

January 14, 2018

Schemes of Work for Maths Teachers As a Head of Maths I understand the importance of a detailed, flexible and simple scheme of work. I designed the Key Stage 3 and GCSE schemes of work for maths teachers available at mr-mathematics.com to be just that. They are fully aligned with the current specifications and are […]

December 19, 2017

Solving Problems with Non-Right-Angled Triangles Solving problems with non-right-angled triangles involves multiple areas of mathematics ranging from complex formulae to angles in a triangle and on a straight line. As the GCSE mathematics curriculum increasingly challenges students to solve multiple step problems it is important for students to understand how to prove, apply and link […]

October 22, 2017

When factorising algebraic expressions with powers students often struggle to identify the highest common factor when it involves an algebraic term. For example, factorising 3h + 12 as 3(h + 4) is attempted correctly much more often than factorising 3h2 + 12h as 3h(h + 4). In this lesson students learn how to identify the […]

## Bryan Hollinworth says:

Quite interesting, succinct and, I would suggest semantic learning methodology.

One of my starter questions went as follows, " If you could have either of the two options, which one would you choose"?

One million pounds, or starting with 1 pence, then double the amount for thirty days thereafter.

This works quite well!

## Robert says:

Hi Jonathan,

I really like your neat explanations of these topics - especially where they are new syllabus requirements/receiving new emphasis.

Many thanks,

Robert