1
Sequence_G8
Question 1
Skill involved: K89a: Determine whether a number is a term in an arithmetic sequence.
Here are the first four terms in a number sequence.
5
8
11
14
Kasey thinks that the number 34 is in this sequence.
Is Kasey correct?
Yes [ ]
No [ ]
(3 marks)
Question 2
Skill involved: K89a: Determine whether a number is a term in an arithmetic sequence.
Determine whether 33 is a term in a sequence that starts with:
3, 5, 7, 9 ...
33 is in the sequence [ ]
33 is not in the sequence [ ]
Question 3
Skill involved: K89b: Determine the term number of a particular term in an arithmetic sequence.
The first four terms of a linear sequence are shown below.
14,17,20,23
Find the position of the term which has the value 77.
+ = …………………………
Question 4
Skill involved: K89c: Determine the term in an arithmetic sequence closest to a particular number.
The first four terms of an arithmetic sequence are shown below.
Dang Minh Tuan
2
13,16,19,22
Find the closest number in the sequence to 81.
…………………………
Question 5
Skill involved: E88: Find the nth term formula for a linear sequence.
Which of the sequences given by the following +th term rules does not contain the number
12345?
27+ + 6 [ ]
13+ + 8 [ ]
5+ + 4 [ ]
2+ + 1 [ ]
Question 6
Skill involved: K88a: Determine the !th term formula of an ascending arithmetic sequence
Find the +th term of the sequence.
4,9,14,19, . . .
+th term = …………………………
Question 7
Skill involved: K88b: Determine the !th term formula of an descending arithmetic sequence.
Find the +th term of the sequence.
5,1, −3, −7, . . .
+th term = …………………………
Question 8
Skill involved: K88c: Determine the !th term formula for shapes in a sequence.
Find an expression for the +th term of the pattern sequence below.
Dang Minh Tuan
3
+th term = …………………………
Question 9
Skill involved: K88d: Determine the !th term formula for an ascending arithmetic sequence
where ! is algebraic.
The first four terms of an arithmetic sequence are shown below.
14,17,20,23
Find an expression for the (+ + 1)th term, in terms of +.
(+ + 1)th term = …………………………
Question 10
Skill involved: E87: Find terms of a sequence given a position-to-term rule.
Here is the rule to find the next term of a sequence.
The first term of this sequence is 12
Find the second term of the sequence.
…………………………
(1 mark)
Question 11
Skill involved: K87a: Generate terms in a sequence using a linear !th term.
The +th term of a sequence is 4+ − 3
Work out the 30th term of the sequence.
…………………………
Dang Minh Tuan
4
Question 12
Skill involved: K87b: Generate the first few terms of a sequence given a linear !th term.
The +th term of a sequence is 2+ + 1
Find the first 4 terms of the sequence.
…………………………
…………………………
…………………………
…………………………
Question 13
Skill involved: K87c: Generate terms in a sequence using a more complex !th term.
The +th term of a sequence is 3+2 + 6+ + 4
Work out the 30th term of the sequence.
30th term = …………………………
Question 14
Skill involved: E89: Determine if a term belongs to a sequence.
The nth term of a sequence is given by 3+ + 5.
Is 21 a term in this sequence?
Yes [ ]
No [ ]
(2 marks)
Question 15
Skill involved: K89a: Determine whether a number is a term in an arithmetic sequence.
Determine whether 66 is a term in a sequence that starts with:
3, 6, 9, 12 ...
66 is in the sequence [ ]
Dang Minh Tuan
5
66 is not in the sequence [ ]
Question 16
Skill involved: K89b: Determine the term number of a particular term in an arithmetic sequence.
The first five terms of a sequence are shown below.
−1,2,5,8,11
Find the position of the term which has the value 53.
+ = …………………………
Question 17
Skill involved: K89c: Determine the term in an arithmetic sequence closest to a particular number.
The first five terms of a linear sequence are shown below.
−2,5,12,19,26
Find the greatest number in the sequence which is less than 105.
…………………………
Question 18
Skill involved: E85: Continue a sequence.
Here are the first five terms of an arithmetic sequence.
2
7
12
17
22
The +th term of a different arithmetic sequence is 4+ + 15
The last term of each sequence is the same number.
There are the same number of terms in each sequence.
Find the number of terms in each sequence.
…………………………
(6 marks)
Dang Minh Tuan
6
Question 19
Skill involved: K88a: Determine the !th term formula of an ascending arithmetic sequence
Find the +th term of the sequence.
6,9,12,15, . . .
+th term = …………………………
Question 20
Skill involved: K88b: Determine the !th term formula of an descending arithmetic sequence.
Find the +th term of the sequence.
4,0, −4, −8, . . .
+th term = …………………………
Question 21
Skill involved: K88c: Determine the !th term formula for shapes in a sequence.
Find an expression for the +th term of the pattern sequence below.
+th term = …………………………
Question 22
Skill involved: K88d: Determine the !th term formula for an ascending arithmetic sequence
where ! is algebraic.
The first four terms of an arithmetic sequence are shown below.
Dang Minh Tuan
7
7,11,15,19
Find an expression for the (+ + 1)th term, in terms of +.
(+ + 1)th term = …………………………
Question 23
Skill involved: E87: Find terms of a sequence given a position-to-term rule.
The +th term of a sequence is obtained by the expression + + 4.
Work out the 23rd term of the sequence.
23$% term = …………………………
Question 24
Skill involved: K87a: Generate terms in a sequence using a linear !th term.
The +th term of a sequence is 1 + 9+
Work out the 90th term of the sequence.
…………………………
Question 25
Skill involved: K87b: Generate the first few terms of a sequence given a linear !th term.
The +th term of a sequence is + − 1
Find the first 5 terms of the sequence.
…………………………
…………………………
…………………………
…………………………
…………………………
Dang Minh Tuan
8
Question 26
Skill involved: K87c: Generate terms in a sequence using a more complex !th term.
The +th term of a sequence is 2+2 + 5+ + 3
Work out the 11th term of the sequence.
11th term = …………………………
Dang Minh Tuan
0
