5. The picture shows a pattern made from triangles. At each stage, two triangles are added: stage 1 contains 4 triangles, stage 2 contains 6 triangles, stage 3 contains 8 triangles, and so on.
(i) Sketch the next two stages of the pattern.
(ii) Draw a table showing the number of triangles needed to complete the first seven stages of the triangle.
(iii) Draw a graph showing the first 10 stages of the pattern. (iv) Find the slope of the graph you have drawn.
(v) What do you notice about the slope of the graph, and the rate at which the number of triangles are increasing?
(vi) Is this a linear pattern? Justify your answer. (vii) What do you notice about the value of the slope of the graph and the first difference in the table?
6. The diagram shows an arrangement of tables and chairs in a linear pattern. 1st stage
Note:
= table and = chair 2nd stage
3rd stage
Stage 1
Stage 2
Stage 3
(i) Draw the next stage of the pattern. (ii) Create a table to show the number of chairs in the first eight stages of the pattern.
(iii) Draw a graph to show the relationship between the number of tables and chairs for the first eight stages of the pattern.
(iv) Find the slope of your graph.
(v) What do you notice about the slope of the graph and the rate at which the number of chairs are increasing?