# Nth Term of Picture Sequences

## Differentiated Learning Objectives

• All students should find the nth term of a picture sequence.
• Most students should use the nth term to work out missing terms in a picture sequence.
• Some students should use the nth term to check whether a diagram is part of a sequence

## Starter/Introduction

Prompts / Questions to consider

• Can you identify the number patterns?
• What is the common difference between each term?
• What does the term n represent?

## Nth Term of Picture Sequences

From the starter activity, students have recalled how to find the nth term from a number sequence. In this lesson, they build on that by modelling a picture sequence using the nth term.

First, demonstrate how to work out the nth term from the table of results for different picture sequences as shown in the video. Students must understand that n represents the other pattern numbers. The nth term is a formula that connects the diagram number to the number of dots in each sequence. When you have found the nth term, ask the class how they can check it works using the data in the table.

Prompts / Questions to consider

• Can you predict what pattern Number 4 would look like?
• What is the common difference between the number of circles for each diagram?
• Does n represent the pattern number or the number of circles in each diagram?
• Can a diagram ever have an odd number of circles?
• How can we use the nth term to find the number of dots in the 50th pattern?
• Is it more efficient to continue the sequence up to 60 dots or to use the nth term?

## Plenary

Prompts / Questions to consider

• Can you predict what pattern Number 4 would look like?
• Do you need to use a table of results to find the nth term, or can you find it using the diagrams?
• Why does n have to be an integer (whole number) to answer part b?
• How many matchsticks does Jack need to make the first 10 diagrams in the sequence?

Ages 14 - 16
##### Nth Term of Arithmetic Sequences

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