Determining the Function from a Quadratic Sequence

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Determining the Function from a Quadratic
Sequence Algebraically!
Gee, I wish I could use my TI 83!
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For each of the following sequences, determine
the common difference and the level at which it
occurs.
1. -3, 0, 5, 12, 21
d 2 at Level D2 ?Quadratic
3 5 7 9
2 2 2

1. 1, -2, -9, -20, -35

-3 -7 -11 -15
d -4 at Level D2 ?Quadratic
-4 -4 -4
3. 6, 10, 14, 18,
d 4 at Level D1 ?Arithmetic
4 4 4
4. - 10, -27, -56, -97
-17 -29 -41
d -12 at Level D2 ?Quadratic
-12 -12
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Now use the function to generate the first four
terms for each of these quadratic functions.
Determine the common difference. What relation
does it have with the coefficient of the a2 term?
Quadzilla


X Y
1 -5
2 -19
3 -41
4 -71
X Y
1 5
2 11
3 19
4 29
d is 2 at D2 a is 1
d is -8 at D2 a is -4
X Y
1 7
2 26
3 57
4 100
X Y
1 -2
2 -8
3 -18
4 -32
d is 12 at D2 a is 6
d is -4 at D2 a is -2
Is there a PATTERN here?
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The Relationship between a d in a Quadratic
Sequence
In a Quadratic Sequence there is a special
relationship between a d!
The difference d from Level D2 is twice the
coefficient of the n 2 or x 2 term in the general
formula.
So to determine the formula or rule for the nth
term of a certain quadratic sequence, we must
first find the common difference and divide by 2
to find the coefficient a!
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The general formula for the nth term of a
quadratic sequence is
Lets determine the first 5 terms
6
To determine the common difference, we subtract
backwards. The first five terms of this sequence
are
7
Now You Try! Use d to determine a and then
solve two equations!
The sequence is 7, 16, 31, 52,
79
9 15 21 27
d2
6 6 6
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STEPS
1. To algebraically determine the formula or
expression for the nth term of a Quadratic
Sequence we need to know the formula.
The Formula for the nth term of a Quadratic
Sequence is
2. We need to know the common difference in
order to determine the coefficient
a.
7, 16, 29, 46, 67
3. We need to use the information from two terms
to set up two equations.
1
2
4. We need to solve the resulting System of
Equations to determine b c
5. We need to replace a, b, c in the general
formula.
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METHOD
1
d 4 so a 2
The Sequence 7, 16, 29, 46, 67
2
Two terms to set up two equations.
3
4
Solve for b c by solving the System of
Equations.
Now we have
SUBTITUTE to find the other variable.
SUBTRACT
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Remember, Homework is not meant to be a burden.
It is meant to help you to reinforce the lesson
and it helps you to remember the steps and proves
whether you understand!
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