Unit 15 Lesson 1

1. Unit 15 –
Algebraic Patterns
1

2. DO NOW
”4 in 4” Unit 15 Pretest
1. Which ordered pair completes 3. What is the rule for the pattern
the table? in the table below? x y
x y
A. x+4
1 6
7 0
B. x–4
A. (2, 16)
2 7
5 4
C. x+5
B. (-1, 16)
3 8
3 8 D. x–5
C. (1, -16)
4 9
1 12
D. (-1, -16)
4. What is the rule for the pattern
2. What pattern is shown in the
in the table below?
table in Question 1? x y
A. Add 2 to each x, Subtract 4 from 2 -1
each y A. x+3
4 1
B. Add 2 to each x, Add 4 to each y B. x–3
6 3
C. Subtract 2 from each x, Subtract C. x●3
4 from each y 8 5
D. x÷3
D. Subtract 2 from each x, Add 4 to
each y
2

3. DO NOW
”4 in 4” 3. What is the rule for the pattern
answers
1. Which ordered pair completes
the table? in the table below? x y
x y
A. x+4
1 6
7 0
B. x–4
A. (2, 16)
2 7
5 4
C. x+5
B. (-1, 16)
3 8
3 8 D. x–5
C. (1, -16)
4 9
1 12
D. (-1, -16)
4. What is the rule for the pattern
2. What pattern is shown in the
in the table below?
table in Question 1? x y
A. Add 2 to each x, Subtract 4 from
2 -1
each y A. x+3
4 1
B. Add 2 to each x, Add 4 to each y B. x–3
C. Subtract 2 from each x, Subtract 6 3
C. x●3
4 from each y
D. x÷3 8 5
D. Subtract 2 from each x, Add
4 to each y 3

4. AIM
What are sequences?
4

5. HOMEWORK
HW #9
Algebra: Linear Functions
Prerequisites worksheet
5

6. MINI LESSON
A sequence is an ordered list of numbers.
Each number is called a term.
An arithmetic sequence is a sequence in
which the difference between any two
consecutive terms is the same.
*adding or subtracting
The difference is called the common
difference. 6

7. MINI LESSON
(cont.)
A geometric sequence is a sequence in
which the quotient between any two
consecutive terms is the same.
*Multiplying or dividing
The quotient is called the common ratio.
7

8. MINI LESSON
(cont.)
Consider the following pattern:
1. Continue the pattern for 4,
5, and 6 triangles. How
many toothpicks are needed
for each case?
2. Study the pattern of numbers. How many toothpicks will you need
for 7 triangles?
3. Continue the pattern for 4, 5,
Now, consider another pattern:
and 6 triangles. How many
toothpicks are needed for each
case?
4. How many toothpicks will you
need for 7 squares? 8

9. WE DO
State whether the following sequences are
arithmetic or geometric. Then state the
common difference or ratio. Finally, write the
next three terms of the sequence.
1. 17, 12, 7, 2, -3, …
2. 96, -48, 24, -12, 6, …
3. 2, 4, 12, 48, 240, …
9

10. YOU DO
State whether each sequence is arithmetic, geometric, or
neither. If it is arithmetic or geometric, state the common
difference or common ratio. Write the next three terms of each
sequence.
1. 2, 4, 6, 8, 10, …
2. 11, 4, -2, -7, -11, …
3. 3, -6, 12, -24, 48, …
4. 20, 24, 28, 32, 36, …
5. 1, 10, 100, 1,000, 10,000, …
6. 486, 162, 54, 18, 6, …
7. 88, 85, 82, 79, 76, …
8. 1, 1, 2, 6, 24, …
9. 1, 2, 5, 10, 17, …
10.-6, -4, -2, 0, 2, … 10

11. YOU DO
(cont.)
State whether each sequence is arithmetic,
geometric, or neither. If it is arithmetic or
geometric, state the common difference or
common ratio. Write the next three terms of each
sequence.
11. 5, -15, 45, -135, 405, …
12.189, 63, 21, 7, 2.3, …
13.4, 6.5, 9, 11.5, 14, …
14.-1, 1, -1, 1, -1, …
11

12. REFLECTION
Identify the sequence that is not the
same type as the others. Explain
your reasoning. 1, 2, 4, 8, 16, …
5, 10, 15, 20, 25, …
125, 25, 5, 1, 1/5, …
-2, 6, -18, 54, -162, …
12