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General rule of a quadratic sequence

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by

Mr Mattock

on 18 September 2015

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Transcript of General rule of a quadratic sequence

General rule of a quadratic sequence
Starter
Find "
a
", the number of
n
in each of the following quadratic sequences.

3, 7, 13, 21, .....

1, 7, 17, 31, .....

1, 3, 6, 10, .....
Finding b and c
L.O. - To find the nth term of a
quadratic sequence (Level 8/EP/ Grade 6).

2
3, 7, 13, 21
4 6 8
2 2
2a =
2
a = 1
a + b + c, 4a + 2b + c, 9a + 3b + c, 16a + 4b + c
3a + b 5a + b 7a + b
2a
2a
3a + b =
4
3 + b =
4
b = 1
a + b + c = 3
1 + 1 + c = 3
c = 1
so an + bn + c = n + n + 1
2
2
1, 7, 17, 31
1, 3, 6, 10
Main Activity 1
Red
Amber
Green
1, 5, 11, 19
4, 9, 16, 25
2, 3, 6, 11
1, 6, 15, 28
2, 11, 26, 47
0, 12, 34, 66
Answers
Red
Amber
Green
5n -3n - 2
2
3n -1
2
2n - n
2
n + n - 1
2
n + 2n + 1
2
(n + 1)
2
n - 2n + 3
2
2, 5, 9, 14
3, 9, 18, 30
1.5n + 1.5n
2
0.5n + 1.5n
2
2, 3 , 6, 9
n + n + 1
2
2
3
3
1
2
3
Finding b and c
3, 7, 13, 21
4 6 8
2 2
a + b + c, 4a + 2b + c, 9a + 3b + c, 16a + 4b + c
3a + b 5a + b 7a + b
2a
2a
Starter
Find "
a
", the number of
n
in each of the following quadratic sequences.

3, 7, 13, 21, .....
2nd difference = 2
a
= 1

1, 7, 17, 31, .....
2nd difference = 4
a
= 2

1, 3, 6, 10, .....
2nd difference = 1
a
=
2
1
2
1, 7, 17, 31
1 7 17 31
6 10 14

4 4
2a =
4
a = 2

3a + b =
6
6 + b =
6
b = 0

a + b + c =
1
2 + 0 + c =
1
c = -1
So the nth term is
2n + 0n - 1 = 2n - 1
2
2
1, 3, 6, 10
1 3 6 10

2 3 4

1 1
2a =
1
a =

3a + b =
2
+ b =
2

b =

a + b + c =
1
+ + c =
1

c = 0
1
2
3
2
1
2
1
2
1
2
So the nth term is

n + n = n + n
2
1
2
1
2
2
2
Plenary
In teams of 3 solve the quadratic patterns exam question.

I will ask someone at random from your
team to explain part, so all need to understand the answer.
Plenary Answers
1 9
25 49

8
16 24
8 8
2a =
8
a =
4

3a + b =
8
12
+ b =
8
b =
- 4

a + b + c =
1
12
-
4
+ c =
1
8
+ c =
1
c =
-7
So the nth term is:

4
n -
4
n -
7
2
Key
Examples

Activities
Activity
Answers

Worked
Example

Worked
Example

Worked
Example
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