Iterative Patterns follow a specific
RULE.
 Examples of Iterative Patterns:

› 2, 4, 6, 8, 10, …
Rule: add 2
Rule: multiply by 2
› 2, 4, 8, 16, 32, …
› 96, 92, 88, 84, 80, … Rule: subtract 4
1/
Rule:
multiply
by
5
› 625, 125, 25, 5, …
Is an Iterative Pattern where the rule is to
ADD or SUBTRACT to get the next term.
 We call the number that you ADD or
SUBTRACT the COMMON DIFFERENCE.
 Examples of Arithmetic Sequences:

› 3, 6, 9, 12, 15…
d=3
› 85, 90, 95, 100, 105, … d = 5
› 5, 3, 1, -1, -3, -5, … d = -2
1.
4, 6, 8, 10, 12, …
1. Yes. d = 2
2.
14, 12, 11, 9, 8, …
2. No
3.
2/
3. Yes, d = 1/9
2/ , 3/ , 4/ , 5/ , 6/ , …
9
9
9
9
9
4.
99, 92, 85, 78, 71, …
5.
½, ¼, 1/8, 1/16, 1/32, …
5. No
6.
9, 6, 3, 0, -3, …
6. Yes. d = -3
9,
1/
3,
4/
9,
5/
9,
2/
3,
…
4. Yes. d =-7
a1 = 2, d = 1
 a1 = 2 means that the first term in your
sequence is 2.
 d = 1 means the common difference is 1.

› Since “1” is positive, you will add “1” each
time to get to the next term in the sequence.

The first 5 terms of the sequence are:
› 2, 3, 4, 5, 6
1.
a1 = 3, d = 7
1. 3, 10, 17, 24, 31
2.
a1 = 0, d = 0.25
2. 0, 0.25, 0.5, 0.75, 1
3.
4.
a1 = 100, d = -5
a3 = 6, d = -4
3. 100, 95, 90, 85, 80
4. 14, 10, 6, 2, -2
Is an Iterative Pattern where the rule is to
MULTIPLY to get the next term.
 We call the number that you multiply the
COMMON RATIO.
 Examples of Geometric Sequences:

› 4, 8, 16, 32, 64, 128, … Rule: r = 2
› 1000, 100, 10, 1, 0.1, … Rule: r = 1/10
› 81, 27, 9, 3, … Rule: r = 1/3
1.
-4, -2, 0, 2, 4, …
1. No
2.
2, 6, 18, 54, 162, …
2. Yes. r = 3
3. 2/3, -2/3, 2/3, -2/3, 2/3,
4.
1, 1.5, 2.25, 3.375, …
5. 3/16, 3/8,
6.
…
¾, 3/2, …
-2, -4, -8, -16, …
3. Yes. r = -1
4. Yes. r = 1.5
5. Yes. r = 2
3/ , 6/ , 12/ ,
16
16
16
6. Yes. r = 2
24/
16



a1 = 24, r = ½
a1 = 24 means that the first term in your
sequence is 24.
r = ½ means that the common ratio is ½.
›

You will multiply each term by ½ in order to
get the next term in the sequence.
The first 3 terms of the sequence are:
›
24, 12, 6
1.
a1 = 4, r = 2
1. 4, 8, 16
2.
a1 = 6, r = 1/3
2. 6, 2, 2/3
3.
a1 = 12, r =
-1/2
3. 12, -6, 3