Sequence and Patterns

Sequence and Patterns

A pattern 

constitutes a set of numbers or objects in which all the members are related with one another by a specific rule. It helps in predicting what comes next in the pattern.

What comes next?

The series of shapes start with a circle, followed by a star, and lastly, a diamond. The series continues in the same pattern. Thus, the next shape after star in the series is a diamond.

What comes next?

In the given list of numbers, there is a certain pattern to follow. The first number is added by 1 to get the second number. Then, the second number is then added by 2 to get the third one. This pattern continues until the last number.

A sequence 

is a list of objects, like numbers, letters, or shapes that follow a particular pattern. The individual element or object in a sequence is called a term.

A sequence can be identified as whether finite or infinite. A finite sequence ends after a certain number of terms while an infinite sequence is a sequence that continues indefinitely, and goes on forever.

Example of Finite Sequence

sequence shows a finite sequence. The sequence represents a multiple of three. Its last term or, in this case, the 6th term is 18. The difference between any two consecutive terms is 3.

Example of Infinite Sequence

The ellipsis or the three dots after the last known term in the sequence represent a sequence without end or an infinite sequence. The word infinite implies endless or without limit.

Study the sequence and determine the next three terms.

The succeeding terms in the sequence can be solved by adding 8 to the previous term. Thus, the next three numbers in the sequence are 29, 37, and 45.

Multiple Choice

It is defined as a set of numbers or objects in which all members are related with each other by a rule.

• sequence

• pattern

• rule

• set

Multiple Choice

What do you call an individual element or object in a sequence?

• term

• sequence

• element

• pattern

Multiple Choice

What is the next term in the sequence?

2, 4, 8, 16, 32, _

• 64

• 108

• 23

• 16

Multiple Choice

Find the next three terms in the sequence:

1, 4, 9, 16, _, _, _

• 25, 36, 49

• 16, 25, 36

• 49, 64, 81

• 9, 16, 25

Problem 1

Loida baked some cookies. She gave six of it to her best friend and left the rest on the table. Joy ate two of them. Then her dad ate three of the cookies. At the end of the day, only five cookies were left on the plate. How many cookies did Loida bake altogether?

To check, use the value obtained in the given problem. That is, from 16, only 10 cookies were left after she gave six to her best friend. Then, only 8 cookies were left after the two cookies were eaten by Joy. Lastly, her dad also ate three of the remaining cookies, so only 5 were left.

Since the value obtained satisfies the given problem, therefore we can conclude Loida baked 16 cookies.

Key Point

In solving a problem or equation, you may look for the pattern used in the problem, work backwards, set up an equation, or use a model.

Multiple Choice

It is used to predict what comes next in a sequence.

• pattern

• sequence

• term

• model

Multiple Choice

• 6

• 16

• 26

• 36

Multiple Choice

• 150

• 15

• 1500

• 105

Multiple Choice

• 2

• 20

• 4

• 42

Multiple Choice

Bernard harvests oranges in his garden. Thirty-five oranges were given to Jake, and 30 were given to Rose. He also gave 16 oranges to his cousin. At the end of the day, he only has 60 oranges in his basket. Find the number of oranges he harvests by solving it backward.

• 130

• 139

• 140

• 141