Download MATH0026 - Day 4 handout

Number Patterns . . . .with pictures!
Look at this pattern of counters
How many counters will there be in the
next pattern?
Here is a table to show the number of
Counters in each shape
Position of shape
Number of counters
1
3
2 3 4
6 9 12
How many counters are added each time?
The term-to-term rule
is + 3
We can also find a position-to-term rule
Shape position
Number of counters
1 2 3 4
3 6 9 12
In words:
number of counters equals 3 × position number
Using algebra:
c=3×n
c = 3n
Can you predict how many counters there
Would be in shape number 20?
Generating Sequences
1.
We can do this by using a term-to-term rule
Generate the first five terms of these sequences
and then describe them in words.
Ist term
10
Term-to-term rule
Add 3
100
Subtract 5
2
double
Generating Sequences
2.
We can also do this by using a position-to-term rule
Write the first five terms of each of these sequences
where the n th term is:
a) n + 3
c) 2n – 0.5
b) 105 – 5n
d) 4n
What is the 20th term for each sequence?
Special Number Sequences
Square Numbers
1×1
2 ×2
3 ×3
4 ×4
1,
4,
9,
16
25,
36, 49 …
These are the first seven square numbers
Special Number Sequences
Cube numbers
1 ×1 ×1
2 ×2 ×2
3 ×3 ×3
1, 8, 27, 64,
125, 216 …
4 ×4 ×4
Special Number Sequences
Triangle numbers
1, 3, 6, 10
15, 21, 28, 36 …
Finding a rule for the n th term
Remember that:
A number sequence
is a set of numbers in a given order
Each number in
the sequence is
called a term
Look at this number sequence:
5, 8, 11, 14, 17 …
We want to find a rule to find the n th term
this will enable us to work out any number in the
sequence, for example, the 50th term, or any term
start by giving each term a position number…
1
2
3
4
5 ….. n
5, 8, 11, 14, 17
What does the sequence go up by?
That’s right,
+3
So what’s the 50th term then?
152
because when n is 50, 3 x 50 + 2 = 152
1
2
3
6
3
4
5 ….. n
12
15 ….
5, 8, 11, 14, 17
9
3n
Because the sequence is adding 3 from one term to
the next, our rule must involve the 3 times table
and to complete the rule, we need to + 2
The complete rule is 3n + 2