12. For the linear pattern shown:
(i) Use a table to show the number of squares in the fi rst fi ve stages of the pattern.
(ii) Represent the table on a graph for the fi rst fi ve stages. (iii) Find a rule, in words, which gives each number in the pattern. (iv) Find a general expression (formula) for the pattern. (v) Find how many squares are in the 53rd stage of the pattern (where n = 52).
13. For the linear pattern shown:
(i) Use a table to show the number of squares in the fi rst four stages of the pattern.
(ii) Represent the table on a graph for the fi rst four stages. (iii) Find a rule, in words, which gives each number in the pattern. (iv) Find a general expression (formula) for the pattern.
14. (i) Copy and complete the following table: x
y Point (–3, –9)
(ii) Plot the points in the table on a Cartesian plane.
(iii) Describe the pattern of the points in words. (iv) State the next point in the pattern.
15. (i) Plot the following points on the Cartesian plane: (–3, 5), (–2, 4), (–1, 3), (0, 2), (1, 1), (2, 0), (3, –1)
(ii) Describe the pattern in words. (iii) Find an expression for the general term for the sequence of x -coordinates. (iv) Find an expression for the general term for the sequence of y -coordinates.
16. Find an expression for the general term for the sequence: 2, 1·5, 1, 0·5, … 17. Find an expression for the general term for the sequence: 1
__ 4 , 1
__ 2 , 3
__ 4 , 1, …
18. The details of the membership of a golf club are shown in the table. To use the golf club facilities, a member must pay the membership fee and then pay a fee upon each visit.
Membership fee Cost per visit
Cost €100 €15
(i) Is there a pattern to the cost of playing at this golf club? Give a reason for your answer. (ii) Copy and complete the table.
Number of visits Start 1 2 3 4 5 Cost
(iii) Find an expression for the general term for the cost of playing at this golf club.
(iv) At the end of her fi rst year, Jane has spent €280 playing at the golf club. How many times did Jane play at the club during her fi rst year?
30 Linking Thinking 2
(v) Find an expression for the general term for the sequence of x values.
(vi) Find an expression for the general term for the sequence of y values.
− 3 − 2 − 1 0 1 2 3 − 9 − 6 − 3 0 3 6 9
Stage 0 (start)
Stage 0 (start)
Stage 1 Stage 1
Stage 0 (start)
Stage 0 (start)
Stage 1 Stage 1
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