Number Pattern Rules

In a pattern table, each row follows a specific arithmetic sequence. If the first row starts with 2 and the common difference is 3, what is the 5th term in the first row?

• 11

• 14

• 17

• 20

A pattern table is constructed such that each element is the sum of its row and column indices. What is the value of the element in the 4th row and 3rd column?

• 5

• 6

• 7

• 8

Consider a pattern table where each column follows a geometric sequence. If the first term of a column is 5 and the common ratio is 2, what is the 4th term in that column?

• 10

• 15

• 20

• 40

The rules for two different patterns that both start with 0 are shown below:
Rule for Pattern G:  Add 4
Rule for Pattern H:  Add 6
Which statement about pattern G and Pattern H is true?

• All of the numbers in pattern G are in pattern H.

• All of the numbers in pattern H are in pattern G.

• The terms in pattern H are always 2 greater than their corresponding terms in pattern G.

• The terms in pattern H are always 1.5 times greater than their corresponding terms in pattern G.

Jeffery writes the number pattern shown below:
5, 9, 13, 17, 21,...
Jeffery's pattern continues.  Whitney also writes a number pattern.  Her pattern has the same starting number as Jeffery's pattern and uses an addition rule.  The first number that both patterns have in common after the starting number is 17.  Which rule could be the rule for Whitney's pattern?

• add 2

• add 4

• add 6

• add 8

Determine a pattern to complete the following table:

• add 4

• add 5

• add 2

• add 8

A necklace has a bead pattern as seen below:
purple: 1, 2, 3, 4, 5, 6, 7...
yellow: 2, 4, 8, ?, ?, 64,128...
What is the correct number of unidentified yellow beads? You may want to use a chart to help you solve the problem.

• 10, 12

• 16, 32

• 8, 10

• 256, 512

The rules for two different patterns that both start with 3 are shown below:
Rule for pattern R: add 4
Rule for pattern S: add 6
What is the 2nd number that the patterns have in common?

• 15

• 9

• 39

• 27

Consider the rules for the two numerical patterns given. Which statement describes the relationship between the two patterns?

• Each term of Pattern B is 2 times the corresponding term of Pattern A.

• Each term of Pattern B is 3 times the corresponding term of Pattern A

• Each term of Pattern A is 6 more than the corresponding term of Pattern B.

• Each term of Pattern B is 6 more than the corresponding term of Pattern A.

Patterns X and Y are generated using these rules. Pattern X starts with 1 and add 4 Pattern Y starts with 2 and add 3 Which set of ordered pairs is generated from corresponding terms of Pattern X and Pattern Y?

• (4, 3) (8, 6) (12, 9)

• (2,1) (5, 5) (8, 9)

• (1, 2) (5, 5) (9, 8)

• (1, 2) (4, 6) (7, 10)