How To Find The Nth Term Of A Geometric Sequence

January 28, 2017

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

When I teach the nth term of geometric sequences I enquire the course 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.

nth term of a geometric sequence

Arithmetic and geometric sequences

I retrieve it's important for students to discover for themselves how a geometric sequence differs from an arithmetic sequence. Students are encouraged to use a estimator to assist 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.

Finding the common ratio

Moving on to the evolution stage I introduce the common ratio past considering the term-to-term rule. For the sequence 2, four, 8, xvi, 32, 64 the common ratio is 2. This means the post-obit term is double the previous term. We begin to generalise this on a term to term basis taking 'a' every bit the first term, a, 2a, 4a, 8a, 16a, 32a.

nth term of a geometric sequence

At present we need to notice the formula for the coefficient of a. Rather than telling the grade the formula I challenge them to derive it independently. The majority of the grade know to heighten ii to a power. A common mistake is to raise 2 to the ability of n. Nosotros discuss what this sequence would look similar (two, four, 8, 16, 32, 64) and after some other 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 exist able to apply it in the future. Click hither to scout the video.

Differentiating geometric sequences for the most able

Equally we work through the remaining questions the common ratio changes from an integer to a fraction. More able students are challenged to detect the first term of a sequence when given 2 other non-sequent terms.

Existent life trouble with geometric sequences

nth term of a geometric sequence

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

Teach this lesson

Sequences through Programming

In my experience students speedily grasp how to find the nth term of an arithmetic sequence. Still, they are frequently unsure what north represents. Teaching sequences through programming addresses this brilliantly.