An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.

Justifying terms of a sequence

Maths

Checking understanding of sequences

Securing understanding of sequences

Formalising a sequence

Generating a sequence using a term-to-term rule

Generating a sequence using a position-to-term rule

Arithmetic sequences

Expressing an arithmetic sequence

Calculating any term

Finding the nth  term

Representing sequences graphically

Problem solving with sequences

The sequences unit allowed pupils to explore different ways of generating sequences and then representing an arithmetic sequence graphically. This serves as an introduction to the future unit on graphical representations of linear equations.

In the prior unit, pupils extended their knowledge of plotting coordinates from KS2 by plotting non-integer values. Pupils learnt that a set of points can satisfy a relationship and this understanding is built on in this unit.

In this unit we develop knowledge of sequences to be able to identify, determine, and continue arithmetic sequences. We finish the unit by looking at how sequences may be reprsented graphically.

Sequences

The sequence 37, 47, 57, 67, 77, ... could be described as which?

14, 19, 24, 29, 34, ... is a translation of a $$5n$$ sequence.

The sequence will always end in the digit 4 or 9 in the ones position.

6941 is an odd number, and the sequence begins with an even number.

Which of the below statements supports the justification that 6941 is not in the arithmetic sequence starting 14, 19, 24, 29, 34, ...?

Which of the below will be common terms in the sequences $$2n+24$$ and $$5n+13$$?

The first 8 terms of a sequence are plotted. Which term is incorrect in the plotting of this arithmetic sequence?

Which of the below is a useful estimation to start with when trying to find 315 in the sequence $$6n-9$$?

881 is not a term because 112.25 is not a whole number.

What does this calculator display tell us?

The calculation 6(20) - 8 would find the 20$$^\text{th}$$ {{}} of the sequence $$6n-8$$.

The terms always end in the digits 1 or 6

The positive terms always end in the digits 1 or 6

Which of these describe features of the sequence $$5n-9$$?

What is the 75$$^\text{th}$$ term of the sequence $$6n-17$$?

You might plot points in all four quadrants.

What happens when you plot an arithmetic sequence?

Calculate the 200$$^\text{th}$$ term of $$17.96-0.32n$$. You may use a calculator.

The 80$$^\text{th}$$ term of the sequence $$6n-35$$

The 50$$^\text{th}$$ term of the sequence $$596-3n$$

The 60$$^\text{th}$$ term of the sequence $$9n-88$$

The 95$$^\text{th}$$ term of the sequence $$5n-11$$

The 50$$^\text{th}$$ term of the sequence $$9n+19$$

Put these term values in order of size. Start with the smallest.

Justifying terms of a sequence

Lesson outcome