Linear and non-linear sequences
Linear sequences together with the nth term
Non- linear sequences together with the nth term
Writing a non- linear sequence into 2 linear sequences
Past examinations examples
Consider the following sequence:
5 , 11 ,17 ,23 … … .
This sequence is called a linear sequences because it has a pattern with a common
difference of 6 .
a) Find the next term of the sequence.
All we need to do is to add 6 to the previous term.
So 23+6=29.
Then we will be asked to find the n th term which is writing the sequence in an algebraic way.
To find the nth term of a linear sequence.
b) Find the nth term of the sequences. The nth term should be:
nth term = (Common difference x n)−¿ the term before the first
nth term= 6 n−1
The nth term can be used to find a particular term in the sequence, because finding the 8 th
term is one thing, finding the 50th term is very demanding to work it out manually.
c) Find the 50th term.
We put 50 instead of n .
6 ( 50 ) −1=299
Example 2. Taken from Past Papers
The following table shows sequence A and sequence B.
a) Find the 6th term of sequence A and sequence B.
1
, Sequence A is made up of square numbers so as regards to sequence A the 6th term is 36.
Sequence B is increasing by 3, 5, 7, 9…..so the 6th term is 45+ 11=56.
b) What is the relationship between terms of Sequence A and Sequence B.
Answer: We are adding 20 all the time with every number in sequence A.
c) Find the nth term of both sequences.
Sequence A is made up of square numbers so the nth term is n2 .
This is a very common sequence so might as well learn it. So sequence B is n2 +20.
We can find the 100th term of both sequence by replacing 100instead of n
d) Consider Sequence A. For what values of n does the term in the sequence take the value
of 900.
n2 =900
n=√ 900
n=30
Example 3. Taken from examination papers
The shapes below are drawn in a pattern.
So shape 5 has 42 tiles and shape 6 has 56 tiles.
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Linear sequences together with the nth term
Non- linear sequences together with the nth term
Writing a non- linear sequence into 2 linear sequences
Past examinations examples
Consider the following sequence:
5 , 11 ,17 ,23 … … .
This sequence is called a linear sequences because it has a pattern with a common
difference of 6 .
a) Find the next term of the sequence.
All we need to do is to add 6 to the previous term.
So 23+6=29.
Then we will be asked to find the n th term which is writing the sequence in an algebraic way.
To find the nth term of a linear sequence.
b) Find the nth term of the sequences. The nth term should be:
nth term = (Common difference x n)−¿ the term before the first
nth term= 6 n−1
The nth term can be used to find a particular term in the sequence, because finding the 8 th
term is one thing, finding the 50th term is very demanding to work it out manually.
c) Find the 50th term.
We put 50 instead of n .
6 ( 50 ) −1=299
Example 2. Taken from Past Papers
The following table shows sequence A and sequence B.
a) Find the 6th term of sequence A and sequence B.
1
, Sequence A is made up of square numbers so as regards to sequence A the 6th term is 36.
Sequence B is increasing by 3, 5, 7, 9…..so the 6th term is 45+ 11=56.
b) What is the relationship between terms of Sequence A and Sequence B.
Answer: We are adding 20 all the time with every number in sequence A.
c) Find the nth term of both sequences.
Sequence A is made up of square numbers so the nth term is n2 .
This is a very common sequence so might as well learn it. So sequence B is n2 +20.
We can find the 100th term of both sequence by replacing 100instead of n
d) Consider Sequence A. For what values of n does the term in the sequence take the value
of 900.
n2 =900
n=√ 900
n=30
Example 3. Taken from examination papers
The shapes below are drawn in a pattern.
So shape 5 has 42 tiles and shape 6 has 56 tiles.
2
