Securing understanding of arithmetic sequences
I can begin to generalise a sequence.
Securing understanding of arithmetic sequences
I can begin to generalise a sequence.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- The n^th term is the generalised way of expressing any term in a sequence.
- For an arithmetic sequence, it will have the form d(n-1)+a
- The a refers to the first term of the sequence.
- The d refers to the common difference between any two consecutive terms.
Keywords
Arithmetic/ linear sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is constant
Common misconception
Misinterpreting the values in an expression for the n^th term. For example, given the n^th term $$3n-5$$ pupils may think that this relates to a sequence that is decreasing by 5 each time
Remind students about how the expression for the n^th term relates to multiples of a number (times tables) and then a shift. For example, 4, 9, 14, 19, ... can be seen as the 5 times table shifted down 1.
To help you plan your year 9 maths lesson on: Securing understanding of arithmetic sequences, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 9 maths lesson on: Securing understanding of arithmetic sequences, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 3 maths lessons from the Non-linear relationships unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Starter quiz
6 Questions
$$3n+2$$ -
$$5, 8, 11, 14, 17, ...$$
$$2n+3$$ -
$$5, 7, 9, 11, 13, ...$$
$$6n-1$$ -
$$5, 11, 17, 23, 29, ...$$
$$6-n$$ -
$$5, 4, 3, 2, 1, ...$$
$$5+n$$ -
$$6, 7, 8, 9, 10, ...$$
$$1-6n$$ -
$$-5, -11, -17, -23, -29, ...$$
Exit quiz
6 Questions
$$3n+9$$ -
$$12, 15, 18, 21, 24, ...$$
$$9n+3$$ -
$$12, 21, 30, 39, 48, ...$$
$$9n-3$$ -
$$6, 15, 24, 33, 42, ...$$
$$3n-9$$ -
$$-6,-3,0,3,6, ...$$
$$9-3n$$ -
$$6,3,0,-3,-6, ...$$