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2.1 Generating sequences

2 Write down the first four terms of each sequence.

a first term is 8 term-to-term rule is ‘subtract 5’
1
1
b first term is 2 term-to-term rule is ‘add 1 ’

2 2

c first term is 4 term-to-term rule is ‘add 1, add 2, add 3, …’

d first term is 24 term-to-term rule is ‘divide by 2’.
3 Zalika is trying to solve this problem.
The tenth term of a linear sequence is 18.
Work out the answer to the problem. The tenth term of a linear sequence is 18.
The term-to-term rule is ‘subtract 4’.
Explain the method you used to solve The term-to-term rule is ‘subtract 4’.
the problem. Work out the fourth term of the sequence.
Shen is trying to solve this problem.
4 Shen is trying to solve this problem. The fifth term of a non-linear sequence is 9.
Work out the answer to the problem.
Work out the answer to the problem.
Explain the method you used to solve The term-to-term rule is ‘divide by 3’.
Explain the method you used to solve
the problem. Work out the second term of the sequence.

5 Use the position-to-term rule to work out the first four terms of each sequence.
a term = position number + 5 b term = 3 × position number − 1
2
c term = position number + 4 d term = 3 × position number 2
6 Use the position-to-term rules to work out:

i the fifth term ii the 10th term iii the 20th term of each sequence.
a term = 4 × position number + 1 b term = position number − 2
2

7 The third term of a sequence is 25. The fifth term of the sequence is 73.
Which of these position-to-term rules is the correct one for the sequence?
2
A term = position number + 16 B term = 5 × position number + 10
C term = 3 × position number – 2 D term = 9 × position number – 2
2
Show how you worked out your answer.
8 This is Shen’s homework. He has spilt tea on some of the questions and answers!

Question 1 The position-to-term rule of a sequence is:
term = 2 × position number +

Work out the first three terms of the sequence.

Answer 1st term = 9 2nd term = 3rd term =
Question 2 The position-to-term rule of a sequence is: term = 5 ×
position number
2
Work out the first three terms of the sequence.
Answer 1st term = 2nd term = 20 3rd term =

Work out the missing answers for Shen. Explain how you worked them out.

2 Sequences and functions 17