Initial Diagnostic Audit - Unit B3: Number Sequences Do NOT use a calculator for any questions in the audit unless specifically told otherwise
Section B3.1 - Simple Number Patterns
What do you think is the next term for each of these sequences?
1.
4, 10, 16, 22, ...
2.
2, 4, 7, 11, 16, ...
3.
5, –1, –7, –13, ...
4.
1, 1, 2, 3, 5, 8, ...
5.
2, 4, 16, 256, ...
Section B3.2 - Recognising Number Patterns
6.
A number sequence begins 1, 5, 6, 11, 17, 28, ...
(a) What is the 7th term of the sequnce?
(b) What is the 8th term of teh sequence?
7. A number sequence begins 2, 9, 28, 65, 126, ...
(a) What is the 6th term of the sequnce?
(b) What is the 7th term of the sequnce?
8.
Here are a series of shapes
Which of the following do you think is the next shape in the series?
Section B3.3 - Extending Number Patterns
What is the 10th term in these sequences:
9.
1, 3, 5, 7, ..., ..., ...
10.
4, 9, 14, 19, ..., ..., ...
11.
1, 2, 4, 7, 11, ..., ..., ...
What is the 20th term in these sequences:
12.
50, 44, 38, 32, ..., ..., ...
13.
1, 4, 9, 16, 25, ..., ..., ...
Section B3.4 - Formulae for Number Sequences
14. What are the first 3 terms of the sequence defined byun = 4n + 1, n = 1, 2, ...
15. Find the 20th term in the sequence un = n 2 – 4, n = 1, 2, ...
16.
The sequence 12, 19, 26, 33, 40, ... is of the form un = an + b , n = 1, 2, ...,
where a and b are constants.
(a) What is the value of a ? a =
(b) What is the value of b ? b =
17. The 4th, 5th and 6th terms of a sequence are 27, 33 and 39.un = an + b , what are the values of a and b ?a = b =
Section B3.5 - General Laws
18. You may use a calculator for this question.
The iterative formula
u n + 1
1 2
un +
7 un
n = 1, 2, ...
can be used, with u 1 = 1, to define a sequence.
(a) What is the value of u 2 ?
(b) What is the value of u 3 ? Give your answer as a decimal
(c) What is the value of u 4 ? Give your answer correct to 3 decimal places
(d) What does the sequence converge to as n increase?
19.
