[The narrator reads out the onscreen text.]

NARRATOR: Question 6. Here are three diagrams made of matches.

[Three diagrams are each made up of a row of diamonds created from matches, their corners touching. The first diagram consists of one diamond, the second of three diamonds and the third of nine diamonds. Each diamond has a horizontal line in the centre.]

NARRATOR: Part a. Write down a sequence of six numbers giving the number of matches in each of these diagrams and the next three in the obvious sequence. Part b. Give the rule for finding the next term from the previous term.

Part a. In the first diagram, we can see that there is 5 matches. In the second diagram there is 15 matches. In the third diagram, there is 45 matches. We can see that in each diagram we are tripling the number of diamond shapes. Each diamond shape is made up of 5 matches. So we begin with 5, we triple 5 to get 15, we triple 15 to get 45. So continuing this pattern, in the fourth diagram, there would be 3 times 45 matches, which is 135. In the fifth diagram, there would be 3 times 135 matches, which is 405. And in the sixth diagram, there would be 3 times 405 matches, which is 1215 matches.

[Part b - Give the rule for finding the next term from the previous term.]

NARRATOR: Part b. We've established that the sequence is 5, 15, 45, 135, 405, 1215. We can see that each term is obtained by multiplying the previous term by 3. For example, Term two - 15 - is 3 times Term one - which is 5. And the pattern continues. So the rule for finding the next term from the previous term can be given by Term n - that is the nth term - is Term (n minus 1) - the term before n - multiplied by 3.

[Term n equals (Term n - 1) times 3.]