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# Defining Sequences

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by

## Mr Mattock

on 20 September 2017

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#### Transcript of Defining Sequences

Defining Sequences
Starter
Two sequences are defined as

3n + 8
5n - 2

After which term does the second sequence become bigger than the first?

Linear Sequences
Find the nth term of this sequence:

3, 10, 17, 24, 31, ...
Linear Sequences (continued)
Find the nth term of this sequence:

26, 22, 18, 14, 10, ...
L.O. - To find the position-to-term rule for a sequence, and use this ability to find formulae.
5, 9, 13, 17, 21, ....

2, 8, 14, 20, 26, ....
18, 11, 4, -3, -10, ...

-3, 4, 11, 18, 25, ...
Main Activity 1
Red
Amber
Green
the width of the pattern and the number of squares
the width of the pattern and the perimeter of the pattern.
Find the nth term of:

3, 7, 11, 15, ....
8, 11, 14, 17, ...
Find the nth term of:
2, 9, 16, 23, ...
23, 16, 9, 2, ...
8, -1, -10, -19, ...
100, 97, 94, 91, ....
Find a formula connecting the number of
rectangles with the number of matchsticks.
Find the nth term of
this sequence:
3, ...., ....., ....., ....., 48
Find the nth term of:

6, 13, 20, 27, 34, ...
9, 15, 21, 27, 33, ...
Find the nth term of:
1, 8, 15, 22, 29, ...
5, 16, 27, 38, 49, ...
Find a formula connecting the number of squares with the perimeter.
2, 11, 20, 29, .....
Find the nth term of the sequence.
Find the first term greater than 100.
111, 102, 93, 84, ....
Find the nth term of the sequence
Find the first negative term of the sequence.
Main Activity 1
Red
Amber
Green
4n -1
3n + 5
7n -1
6n + 3
7n -6
11n -6
P = 3s + 1
7n - 5
-7n + 30 (30 - 7n)
-9n + 17 (17 - 9n)
-3n + 103 (103 - 3n)
9n - 7
101 (12th term)
9n - 6
-9n + 130 (130 - 9n)

-5 (15th term)
M = 11r
Linear Sequences
Find the nth term of these linear sequences
Linear Sequences (continued)
Starter
Two sequences are defined as

3n + 8 = 11, 14, 17, 20, 23,
26
, 29, 32, ...
5n - 2 = 3, 8, 13, 18, 23,
28
, 33

After which term does the second sequence become bigger than the first?
After the 6th term
the width of the pattern and the number of squares. -
S = 2w - 1

the width of the pattern and the perimeter of the pattern. -
P = 4w
Linear Sequences
Find the nth term of this sequence:

3, 10, 17, 24, 31, ...
= 7n - 4
7, 14, 21, 28, 35, ... = 7n
5, 9, 13, 17, 21, ....
= 4n + 1

2, 8, 14, 20, 26, ....
= 6n - 4
Linear Sequences
Find the nth term of these linear sequences
4 8 12 16 20 .... = 4n
6 12 18 24 28 .... = 6n
Linear Sequences (continued)
Find the nth term of this sequence:

26, 22, 18, 14, 10, ...
= -4n + 30 = 30 - 4n
-4, -8, -12, -16, -20, ... = -4n
18, 11, 4, -3, -10, ...
= -7n + 25

-3, 4, 11, 18, 25, ...
= 7n - 10
Linear Sequences (continued)
-7,-14, -21, -28, -35, ... = -7n
7, 14, 21, 28, 35, ... = 7n
Activities
Activity

Key
Examples

Worked
Example

Worked
Example

Worked
Example

Worked
Example
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