Linear Patterns on the TI-84
Task: What if I start on 10 on the number line and I step 3 numbers every step that I take. What
numbers will I land on?
This question is an example of an arithmetic sequence. (An arithmetic sequence is a sequence in which
each term is equal to the preceding term plus a constant. This constant is called the common difference.
Arithmetic sequences are of the form An = An-1 + D, where D is a constant. The tenth term of a sequence
is noted as A10 (read as A sub 10). The nth term (An) is called the general term of the sequence.) I don’t
give students this formula! An arithmetic sequence when listed in ordered pairs will always be a linear
pattern (equation) so I approach these problems in that manner.
I have the students to represent the data in a table like this:
N
Value
or
Step Number Landing
1
13
1
13
2
16
2
16
3
19
3
19
4
22
4
22
5
25
5
25
Activity sheet #1 that follows has the students complete charts using the same technique that we used on
this sample. Page 2 asked the student to find the start value and the constant term when given the
sequence of numbers. Page 3 asks them to find the start and constant values, plot a scatterplot, and then
by trial-and-error find the equation that passes through these points.
This activity is laying the foundation for finding linear equations from a table where the constant
number is the coefficient of X and the start number is the constant in the equation. For example, in the
above example the Y = 3X + 10.
Patterns on the TI-84
page 1
1. Start: 1 Constant: +3
Step # Landing
1
2
3
4
5
5. Start: 5
Step #
1
2
3
4
5
Constant: +2
Landing
2. Start: -6 Constant: +2
Step # Landing
1
2
3
4
5
6. Start: 7
Step #
1
2
3
4
5
Constant: +3
Landing
3. Start: 1
Step #
1
2
3
4
5
Constant: +2
Landing
7. Start: 12 Constant: -3
Step # Landing
1
2
3
4
5
4. Start: 6
Step #
1
2
3
4
5
Constant: +1
Landing
8. Start: 11 Constant: -4
Step # Landing
1
2
3
4
5
Patterns on the TI-84
1. Start: ___
Constant: ___
Step # (X) Landing (Y)
1
1
2
4
3
7
4
10
5
13
2. Start: ___
Step # (X)
1
2
3
4
5
3. Start: ___
Constant: ___
Landing (Y)
6
11
16
21
26
Constant: ___
Step # (X) Landing (Y)
1
19
2
17
3
15
4
13
5
11
4. Start: ___
Constant: ___
Step # (X) Landing (Y)
1
6
2
7
3
8
4
9
5
10
page 2
5. Start: ___
Constant: ___
Step # (X) Landing (Y)
1
3
2
7
3
11
4
15
5
19
6. Start: ___
Constant: ___
Step # (X) Landing (Y)
1
7
2
9
3
11
4
13
5
15
7. Start: ___
Constant: ___
Step # (X) Landing (Y)
1
2
2
5
3
8
4
11
5
14
8. Start: ___
Constant: ___
Step # (X) Landing (Y)
1
17
2
13
3
9
4
5
5
1
Patterns on the TI-84
page 3
a) Determine the Start number and the Constant for each table of values.
b) Use your calculator to draw a scatterplot for the points in each table.
c) Find the equation for the line that passes through all of the points in your scatterplot.
1. X
1
2
3
4
5
Y
5
8
11
14
17
2. X
1
2
3
4
5
Y
1
3
5
7
9
3. X
1
2
3
4
5
Y
12
10
8
6
4
Start: _______
Constant: ________
Start: _______
Constant: ________
Start: _______
Constant: ________
Equation: ___________
Equation: ___________
Equation: ___________
4. X
1
2
3
4
5
5. X
1
2
3
4
5
Y
9
14
19
24
29
Y
7
4
1
-2
-5
6.
X
1
2
3
4
5
Y
3
3.5
4
4.5
5
Start: _______
Constant: ________
Start: _______
Constant: ________
Start: _______
Constant: ________
Equation: ___________
Equation: ___________
Equation: ___________
Describe the relationship between the Start number, the Constant, and the Equation.
Predict the equation that would pass through these points.
X
1
2
3
4
5
Y
9
12
15
18
21