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

The nth term of a sequence is the position of a term in a sequence where n stands for the term number.

Problem solving with sequences

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

Justifying terms of a sequence

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

Which would describe the sequence 1,3,6,10,15, ...?

The 2$$^\text{nd}$$ term of an arithmetic sequence is 11 and the 6$$^\text{th}$$ term is 47. What is the 1$$^\text{st}$$ term of the sequence?

Buses leave Wallsend for Byker at regular intervals. The second bus of the day leaves at 6:44 am. You just missed the seventh bus of the day which left at 8:04 am. What time is the next bus?

The 24$$^\text{th}$$ term of an arithmetic sequence is 281. The 37$$^\text{th}$$ term is 437. Which calculation will be the starting point to finding the $$n^\text{th}$$ term of the sequence?

It's not an arithmetic (linear) sequence we can't write an $$n^\text{th}$$ term.

What is the $$n^\text{th}$$ term of this sequence?

How many triangles are there in this pattern? Don't forget to count all triangles of all sizes.

Which words would describe the sequence 1,4,9,16,25, ...?

What is the next term in the arithmetic sequence starting -19,-12,-5,2 ...

Buses leave for Finchley Park every 25 minutes. If a bus just left at 7:41 am what time will the next bus leave?

What is the $$n^\text{th}$$ term of the arithmetic sequence 8,9,10,11, ...?

What is the $$n^\text{th}$$ term of the arithmetic sequence 8,11,14,17 ...?

The 118$$^\text{th}$$ term of the sequence $$5050-7n$$ is 4224. What is the 113$$^\text{th}$$ term?

Problem solving with sequences

Lesson outcome