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2.2 Finding the nth term

) Exercise 2.2

1 The nth term of a sequence is 3n. Work out the first three terms and the 10th term of the sequence.

2 The nth term of a sequence is 6 − n. Work out the first three terms and the 20th term of the
sequence.
3 The nth term of a sequence is 4n + 7. Work out the first three terms and the 50th term of the

sequence.

4 The nth term of a sequence is 10n − 8. Work out the first three terms and the 100th term of the

sequence.
5 Match each yellow sequence card with the correct blue nth term expression card.

C –3, –2, –1, 0, ... E 6, 8, 10, 12, ...
A 8, 9, 10, 11, ... D 7, 14, 21, 28, ... F 2, 6, 10, 14, ...
B 4, 8, 12, 16, ...

iii 4n – 2
ii 2n + 4
i n – 4 v 7n vi n + 7
iv 4n

6 Work out an expression for the nth term for each sequence.
a 3, 5, 7, 9, … b 5, 8, 11, 14, … c 4, 9, 14, 19, …
d 2, 10, 18, 26, … e 8, 6, 4, 2, … f 11, 7, 3, −1, …
g −2, −7, −12, −17, … h −3, 6, 15, 24, … i 23, 35, 47, 59, …
7 Use the nth term expression to work out the 100th term of each sequence in question 6.

8 Tanesha and Jake are looking at the number sequence.
1
1
4, 4 , 5, 5 , 6, ...
2
2
I think the expression for the nth
1
term of this sequence is 4n + . I think the expression for the nth
2
1
term of this sequence is n + 4.
2

Is either statement correct? Explain your answer.
9 Look at this number sequence. 24, 18, 12, 6, 0, ...

By just looking at the numbers in the sequence, explain why you can tell that the nth term
expression for this sequence cannot be 6n + 18.
10 This pattern is made from green squares.

Pattern 1 Pattern 2 Pattern 3 Pattern 4

Razi thinks that the nth term for the sequence of numbers of green squares is 3n + 2.
Is Razi correct? Explain how you worked out your answer.

2 Sequences and functions 19