find the next three terms in the pattern: 1, 4, 7,
TRANSCRIPT
...,13,11,7,3
12 xy
Find the next three terms in the pattern:
1, 4, 7, . . .
Find the tenth term in the pattern:
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 10th ?
The tenth term is
282828282828
Now find the one-hundredth term:
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 100th ?
You don’t really want to write out 100 terms, do
you?
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 100th ?
If so, go ahead and find the 1,000th term.
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 1000th ?
If not, we need to find a better way.
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 1000th ?
One way would be to write an equation which maps
the number’s rank . . .
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 1000th ?
. . . onto the number itself.
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 1000th ?
Now 4 will map onto 10,
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 1000th ?
and so forth. 6 will map onto 16,
And 6 will be an x-value
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 1000th ?
to correspond with a y-value of 16.
How can we write the equation?
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 1000th ?
.drawkcab krow s’teLLet’s work backward. .drawkcab krow s’teL
We can start with an equation,
24 xy
and see what pattern develops.
2xy
1 2610
3
24 xy
? ??
each time xWhat happens to y
2xy
1 2610
3
increases by 1?
Each time x increases by 1,
2xy
1 2610
3
y increases by 4.
Look at the equation we used to get those
numbers.24 xy
Notice the 4.
24 xy
Let’s try this equation:
13 xy
Predict what y will do as x increases by 1.
??2xy
1 25 8
3?
13 xy
There is a pattern working here.
The amount y changes each time x increases
by 1 is part of the equation.
So if we go back to the pattern we started with:1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 100th ?
1xy
1 24 7
3
We see that y increases by 3 each time x increases by 1,
and we can start writing the equation.
...3xy
We can get y by multiplying x by 3,
1xy
1 24 7
3
and then adding or subtracting some
number.
1xy
1 24 7
3
bxy 3 ...3xy
When we use 1 for x,
1xy
1 24 7
3
bxy 3
we know that y is also 1,
1xy
1 24 7
3
so we get,
bxy 3b31
1xy
1 24 7
3
b31
What does b have to be to make the equation true?
bxy 3231
2b
Now we can complete the equation.
bxy 3
23 xy
What is the 100th term in the pattern?
23 xy
1,1st 2nd 3rd 4th 5th 6th
4, 7, 10, 13, 16, . . . 100th ?
21003 y 2300 y 298y
These are the steps we took to write the
equation:
2xy
3 42 6
5
1. Find the change in y each time x changes by 1.
2xy
3 42 6
5
2. Begin writing the equation, , using the change in y as m.
bmxy
2xy
3 42 6
5
bxy 4
3. Calculate b, using the numbers from our
table.
2xy
3 42 6
5
bxy 4
bx 46
3. Calculate b, using the numbers from our
table.
2xy
3 42 6
5
3. Calculate b, using the numbers from our
table.
2xy
3 42 6
5
bx 46
b 546
3. Calculate b, using the numbers from the
table.
2xy
3 42 6
5
b 206 14b
4. Write the final equation.
2xy
3 42 6
5
bxy 4 144 xy
Write the equation:
1.
20xy
1 215 10
3
4xy
1 114 24
3
...,8,4,0,4
2.
3.
Answers:
1.
20xy
1 215 10
3
4xy
1 114 24
...,8,4,0,4
2.
3.
84 xy
255 xy
95 xy
3
*Press Enter
4xy
1 114 243.
95 xy
3
Did you notice that x is increasing by 2, not one?If y increases 10 every
time x increases 2,what is the increase in y
as x increases 1?