Study Guide #2
7.16abcde
7.2
Properties
Sequences
Name: ____________________________________ Date: _______________ Block: _______
This test covers learning targets related to Arithmetic and Geometric sequences. The test also covers justifying and
identifying the properties in equations, simplifying expressions and modeling the following real number properties
numerically (with numbers), algebraically (with variables or letters), and in abstract expressions or pictures:
Commutative Properties of Addition and Multiplication,
Associative Property of Addition and Multiplication,
Identity Properties of Addition and Multiplication,
Additive Inverse Property,
Inverse Property of Multiplication,
Zero Property of Multiplication, and the
Distributive Property,
Know How To:
I.
o
Number Properties
Differentiate between all 10 number properties covered in the unit.
 Commutative Property of Addition and Multiplication (Order Property) states changing the
order of the addends or factors does not change the sum or product.
Example 1: 1 + 2 = 2 + 1; a + b = b + a
Example 2: 25 + 154 +75 = 25 + 75 +154 commutative property of (+)
=100 + 154 add
=254
simplify
Example 3: 3(4) = 4(3); xy =yx
Example 4: 5· 635 2 = 5· 2 · 635 commutative prop of (x)
= 10 · 635 multiply
= 6350
simplify
 The Associative Property of Addition and Multiplication(The Grouping Property) states
changing the grouping of addends does not change the sum.
Example 1: (a + b) + c = a + (b + c)
Example 2: (3 + 4) + 6 = 3 + ( 4 + 6) associative prop of (+)
= 3 + 10 add
= 13
simplify
Example 3: (a·b)·c = a·(b·c)
Justify operations w/properties
Example 4: (3·4)·6 = 3·(4·6) associative prop of (x) Justify operations w/properties
= 3·10
multiply
= 30
simplify
 The Identity Property of Addition states the sum of zero and any number a is a.
Example 1: 5 + 0= 5
 The Identity Property of Multiplication states the product1 and any number a is a.
Example 2: 1·a=a
Study Guide #2
SOLs: 7.16abcde – Properties
7.2 - Sequences
 Multiplication Property of Zero states zero multiplied by a number is always zero.
Example 3: 0·b=0
Multiplicative Inverse Property states that the product of a number and its reciprocal or multiplicative
inverse is 1. Remember the reciprocal is the flip of the fraction. An integer becomes a fraction by
putting it over 1, ex. 2/1.
Example: 2∙(1/2) = 1; (3/4)∙(4/3) = 1
 Additive Inverse Property states two integers that are opposites of each other are called
additive inverses. The sum of any number and its additive inverse or opposite is zero.
Examples: a + (-a) = 0
4 + (-4) = 0; 4 and -4 are opposites
-x + x = 0; -x and x are opposites too.
Name the property shown.
1. ______________________________
2. ______________________________
3. ______________________________
4. ______________________________
5. ______________________________
SOLs: 7.16abcde – Properties
7.2 - Sequences
Study Guide #2
II.
Sequence: is an ordered list of numbers. Each number in the sequence is a term.
 Arithmetic Sequence: is a sequence in which the difference (common difference) between any two
consecutive terms is the same. To find the next term add the common ratio to the last term.
Example: 3,
5,
7,
9,
11…
+2
+2
+2
+2
 Geometric Sequence is a sequence in which the quotient (common ratio) between any two consecutive
terms is the same. To find the next term multiply the next term by the common ratio.
Example: 2,
6,
18,
54…..
x3
x3
x3
See next pages…
SOLs: 7.16abcde – Properties
7.2 - Sequences
Study Guide #2
Section 1: Properties
Directions: Show 3 examples of each of the 10 properties. One example should be numerical, one
algebraic, and one abstract (a picture).
Commutative Property of Addition
Commutative Prop. of Multiplication
Associative Property of
Multiplication
Identity Property of Addition
Identity Property of Multiplication
Distributive Property
Multiplicative Property of Zero
Inverse Property of Addition
Inverse Property of Multiplication
Directions: Write the name of the property on the line. You may abbreviate except for Identity & Inverse.
f+0=f
___________________________________________________________
10 x 1 = 10
___________________________________________________________
(5 + 3) x 0 = 0
___________________________________________________________
5
x
6
6
=1
5
4 + (-4) = 0
4(3 + 2) = 12 + 8
___________________________________________________________
___________________________________________________________
___________________________________________________________
A+(B+C) = (A+B)+C ___________________________________________________________
8+(2+3)=8+(3+2)
(4x3)6 = 4(3x6)
3 + 4 = 4 +3
___________________________________________________________
___________________________________________________________
___________________________________________________________
Directions: Each of the expressions below has been partially simplified. Identify the property
that was used to simplify them:
1) 4k + 5(x – 3)
4k + 5x – 15
(property)
2) 3 + (4 ∙ 2)
3 + (2 ∙ 4)
(property)
3) 4(20 + 0)
4(20)
(property)
4) 4 + (5 + -5)
4+0
(property)
SOLs: 7.16abcde – Properties
7.2 - Sequences
Study Guide #2
Justify with the correct properties.
1. 3 + 2(1/2 + 0)
= 3 + 2(0 + 1/2)
= 3 + 2∙0 + 2∙1/2
____________________
____________________
= 3 + 0 + 2∙1/2
____________________
=3+0+1
____________________
=3+1
____________________
=4
Simplify_____________
Section 2: Sequences
Directions: There are two types of sequences: arithmetic and geometric. Create an example for each
and identify the pattern.
Arithmetic Example:
_____
_____
_____
_____
_____
Geometric Example:
_____
_____
_____
_____
_____
pattern is: ____________
pattern is: ____________
Describe the pattern in each sequence and identify the sequence as arithmetic, geometric, or neither.
Then write the next three terms.
1.)
5, 9, 13, 17…
Pattern: ________________________________________________
(Circle one)
Arithmetic
Geometric
Neither
Next three terms: ________________ , _________________, _______________
2.) 90, 91, 94, 99…
Pattern: ________________________________________________
(Circle one)
Arithmetic
Geometric
Neither
Next three terms: ________________ , _________________, _______________
SOLs: 7.16abcde – Properties
7.2 - Sequences
Study Guide #2
3.)
9.1, 8.4, 7.7, 7.0…
Pattern: ________________________________________________
(Circle one)
Arithmetic
Geometric
Neither
Next three terms: ________________ , _________________, _______________
4.)
0.2, 0.4, 0.6, 0.8…
Pattern: ________________________________________________
(Circle one)
Arithmetic
Geometric
Neither
What is the 6th term in this sequence? __________
5.)
405, 135, 45, 15
Dylan began his number pattern with 405. To determine each new number in the pattern, he
performed the same operation on the previous number. Which operation could have been used for
the pattern?
A. Multiply by 3
B. Multiply by 1/3
C. Subtract 270
D. Divide by 5
6.) Dave states that 1, 10, 2, 20, 3, 30, … is not a geometric sequence. Do you agree? Explain. Explain.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________