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End-of-unit review

End-of-unit review

1 Is the sequence 15, 14, 12, 9, ... linear or non-linear? Explain your answer.
2 The eighth term of a linear sequence is 26. The term-to-term rule is ‘add 3’.
Work out the fourth term of the sequence.
Explain the method you used to solve this problem.
3 The fifth term of a non-linear sequence is 324. The term-to-term rule is ‘multiply by 3’.
Work out the second term of the sequence.
Explain the method you used to solve this problem.
4 A sequence follows the position-to-term rule: term = 2 × position number − 2.
2
Work out:
i the first four terms ii the 10th term iii the 20th term.
5 Work out an expression for the nth term for each sequence.
a 5, 7, 9, 11, … b 10, 8, 6, 4, … c −8, −5, −2, 1, …
6 Look at this number sequence.
Maha thinks that the nth term expression for this sequence 4, 10, 16, 22, …
cannot be 10 − 6n.
Explain why she is correct.
7 This pattern is made from pink dots.

Pattern 1 Pattern 2 Pattern 3 Pattern 4

Alicia thinks the expression for the nth term for the sequence of the numbers of pink dots is 4n + 2.
Anders thinks it is 2n + 2. Oditi thinks it is n + 3.
Who is correct? Explain how you worked out your answer.

8 Work out the inverse function for each equation.
a y = x − 2 b y = 8x c y = x + 2 d y = x +1
5 2
9 Work out the inverse function for each mapping.
x
a x → x + 1 b x → c x → 3x − 7 d x → x + 2
4 10
10 Dakarai thought of a number. He subtracted 11 from the number then divided the result by 4.
a Use a mapping to write this as a function.
Dakarai’s answer was −1.2.
b Use inverse functions to work out the number Dakarai thought of. Show all your working.
11 Sasha thought of a number. She added 22.5 to the number then multiplied the result by 2.
a Write this as a function as a mapping.
Sasha’s answer was 50.
b Use inverse functions to work out the number Sasha thought of. Show all your working.

22 2 Sequences and functions