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.

n1234
5n5 1 = 55 2 = 105 3 = 155 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.

n1234
7n - 3 71 - 3 = 472 - 3 = 11 73 - 3 = 1874 - 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 Click on this button below to see the correct answer 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 Click this button to see if you are correct 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 Click on this button to see the correct answer 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.

(a) 3n

(b) 9n

(c) n+4

(d) 2n+1

(e) 3n + 4

(f) 5n - 2

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.

(a) What is the 10th term of the sequence 2n + 1?

(b) What is the 8th term of the sequence 3n + 6?

(c) What is the 5th term of the sequence 4n + 1?

What is the 7th term of the sequence 5n - 1?


You have now completed Unit 7 Section 3
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Produced by A.J. Reynolds January 2001