Patterns to Equations

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Patterns to Equations
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Find the next three terms in the pattern
1, 4, 7, . . .
13,
16
10,
1, 4, 7,
3
Find the tenth termin the pattern
1,
4,
7,
10,
13,
16,
. . .
1st
2nd
3rd
4th
5th
6th
10th ?
4
The tenth term is...
28!
1,
7,
16,
19,
22,
4,
10,
13,
25,
5
Now find theone-hundredth term
1,
4,
7,
10,
13,
16,
. . .
1st
2nd
3rd
4th
5th
6th
100th ?
6
You dont really want to write out 100 terms, do
you?
1,
4,
7,
10,
13,
16,
. . .
1st
2nd
3rd
4th
5th
6th
100th ?
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If so, go ahead andfind the 1,000th term.
1,
4,
7,
10,
13,
16,
. . .
1st
2nd
3rd
4th
5th
6th
1000th ?
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If not, we need tofind a better way.
1,
4,
7,
10,
13,
16,
. . .
1st
2nd
3rd
4th
5th
6th
1000th ?
9
One way would be to write an equation which
calculates the y-value . . .
for any x-value.
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The Pattern as Ordered Pairs.
x 1, y 1
x 2, y 4
x 3, y 7
1,
4,
7,
10,
13,
16,
. . .
1st
2nd
3rd
4th
5th
6th
1000th ?
11
Look for a pattern.
Put the x and y-values in a table and look for a
pattern...
12
Does the pattern workfor larger numbers?
13
As x increases by 1, y increases by 3.
As x increases by 3, y increases by 9.
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Note The slope is the same between x 1 2,
between x 2 3, between x 3 6
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So, if y mx b, and m (slope) 3, then
equation must be
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To find b,
Take any known (x, y) pair, plug in the values
for x y and solve for b.
17
Solve
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Now we can complete the equation.
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What is the 100th term in the pattern?
20
Review the steps with a new example
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Find the change in yover the change in x (slope).
1
1
-4
-4
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Begin writing the equation,
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Use one (x, y) pair from the table, substitute
and solve the equation for b.
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Write the final equation with m and b.
m -4
b 14
25
Write the equation
1.
2.
3.
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Answers
1.
2.
3.