Download Linear sequences

Linear sequences
A linear sequence is a list of numbers that
have a common difference between each
number in the list.
Finding the rule that can extend the
sequence from the previous term is called
the term to term rule.
This is a basic requirement of sequences
but we need to extend our knowledge.
Write down the rule and fill in the spaces.
1.
4
10
16
2.
2
3.5
5
3.
32
25
18
22
6.5
11
28
…… ……
…… ……
…… ……
Position to term rules
It is important to be able to find the number in a
sequence from its position in that sequence.
Example.
If we want to find the 100th term in the sequence
2, 6, 10, 14,18………
Do we need to keep adding 4, until we find the
100th number in the sequence!!
Any suggestions?
1,
2,
3,
4,
5 ……………….Position in sequence (n)
2, 6, 10, 14, 18 ………………. Common difference = 4
4, 8, 12, 16, 20………………. Numbers in 4 x table (4n)
To find numbers in sequence multiply position by 4 and take 2
nth Term = 4n – 2
100th term = (4 x 100) – 2
= 398
1,
2,
3,
4,
5 ……………….Position in sequence (n)
8, 13, 18, 23, 28 ………………. Common difference = 5
5, 10, 15, 20, 25………………. Numbers in 5 x table (5n)
To find numbers in sequence multiply position by 5 and add 3
nth Term = 5n + 3
100th term = (5 x 100) + 3
= 503
For each of the number sequences below, find a rule for the nth
term (tn) and work out the value of t100.
Question 1
8, 13, 18, 23, 28, tn= 5n + 3
Question 2
1, 4, 7, 10, 13,
tn= 3n - 2
t100= 3 x 100 - 2 = 298
Question 3
2, 9, 16, 23, 30, tn= 7n - 5
t100= 7 x 100 - 5 = 695
Question 4
9, 15, 21, 27, 33, tn= 6n + 3
t100= 6 x 100 + 3 = 603
Question 5
-1, 4, 9, 14, 19,
tn= 5n - 6
t100= 5 x 100 - 6 = 494
Question 6
-3, 1, 5, 9, 13,
tn= 4n - 7
t100= 4 x 100 - 7 = 393
Question 7
6, 18, 30, 42, 54, tn= 12n - 6
t100= 5 x 100 + 3 = 503
t100= 12 x 100 - 6 = 1194
Using an nth term to generate a sequence
14 May 2017
If an nth term is given, it is possible to work out any value in the
sequence.
It is likely that a question may ask you to generate the first five terms
of a sequence from an nth term.
Example
Find the first five terms of the sequence from the following n th terms.
1. 4n + 2
6, 10, 14, 18, 22
2. 7n – 4
3, 10, 17, 24, 31
3. 12n – 5
7,19, 31, 43, 55