Unit 7 Section 3 : Generating Number Sequences

In this section you will find out how a formula can be used to give the terms of a sequence.

Example 1
The formula 5n describes a sequence.
To find out what the sequence is, we need to let n have the values 1, 2, 3, 4, ...
Remember, 5n means 5 × n.

n 1 2 3 4

5n 5 × 1 = 5 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20

So the sequence given by 5n is 5, 10, 15, 20, ...

Example 2
The formula 7n - 3 also describes a sequence.
Again, we need to let n have the values 1, 2, 3, 4, ...
Remember, 7n - 3 means (7 × n) - 3.

n 1 2 3 4

7n - 3 7×1 - 3 = 4 7×2 - 3 = 11 7×3 - 3 = 18 7×4 - 3 = 25

So the sequence given by 7n - 3 is 4, 11, 18, 25, ...

We say that 7n - 3 is the general term of the sequence.
The value of n corresponds to the position in the sequence.

Example Question

Work out the answer to each of these questions then click on the button marked

to see whether you are correct.

(a) What sequence is generated by the general term 5n - 1?

(b) What sequence is generated by the general term 6n + 2?

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the

button to find out whether you have answered correctly. If you are right then

will appear and you should move on to the next question. If

appears then your answer is wrong. Click on

to clear your original answer and have another go. If you can't work out the right answer then click on

to see the answer.

Question 1
The first two questions in this exercise are to help you revise number machines.
Work out what number would come out of each of the following number machines.

(a)
(b)
(c)

(d)
(e)
(f)

Question 2
Work out what number was put into each of these number machines to get the answer shown.

(a)
(b)
(c)

(d)
(e)
(f)

Question 3
The sequence 1, 2, 3, 4, 5, ... is put into each of these number machines.
Write down the first five terms of the sequence that comes out of each machine.
Remember to put commas between each term.

The sequence is

The sequence is

The sequence is
Which machine gives the even numbers?

Question 4
Now you will generate sequences using a formula instead of a number machine.
If you have forgotten how to do this then look back at the examples at the beginning of this section.

Write down the first five terms of the sequence given by each of the formulae below.
Remember to put commas between each of the five terms.

Question 5
Answer these questions about various sequences.
You may need to write out the sequence but it is possible to answer the questions without doing so.

You have now completed Unit 7 Section 3

Your overall score for this section is

Correct Answers
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Incorrect Answers
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There were questions with wrong answers.
There were questions you didn't attempt.

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Produced by A.J.Reynolds January 2001

n	1	2	3	4
*7n - 3*	7×1 - 3 = 4	7×2 - 3 = 11	7×3 - 3 = 18	7×4 - 3 = 25