A sequence is simply a list of numbers that are arranged in a certain order.
You can think of it like a group of numbers that follows a specific pattern. Each number in this list is called a "term." These terms are usually counted starting from 1 or 0.
Let’s break it down:
What is a Sequence? A sequence is like a rule that only uses whole numbers. Most often, these are the positive numbers or all whole numbers.
How to Write a Sequence: We can show a sequence like this: ( a_1, a_2, a_3, \ldots ) or we can write it as ( a_n ). Here, ( n ) tells you which term it is in the list.
A Simple Example: A very basic sequence is the list of even numbers: ( 2, 4, 6, 8, \ldots ). This can be written with a rule: ( a_n = 2n ).
Different Types of Sequences:
Arithmetic Sequence: This is a sequence where the difference between each term is the same. For example, in the sequence ( 3, 6, 9, 12, \ldots ), we add 3 each time (this is called the common difference).
Geometric Sequence: In this type, you find each term by multiplying the previous term by a certain number. For example, in the sequence ( 2, 6, 18, 54, \ldots ), you multiply by 3 each time (this is called the common ratio).
It's important to understand sequences because they help us learn about series later on. Series are just the sums of the terms in a sequence!
A sequence is simply a list of numbers that are arranged in a certain order.
You can think of it like a group of numbers that follows a specific pattern. Each number in this list is called a "term." These terms are usually counted starting from 1 or 0.
Let’s break it down:
What is a Sequence? A sequence is like a rule that only uses whole numbers. Most often, these are the positive numbers or all whole numbers.
How to Write a Sequence: We can show a sequence like this: ( a_1, a_2, a_3, \ldots ) or we can write it as ( a_n ). Here, ( n ) tells you which term it is in the list.
A Simple Example: A very basic sequence is the list of even numbers: ( 2, 4, 6, 8, \ldots ). This can be written with a rule: ( a_n = 2n ).
Different Types of Sequences:
Arithmetic Sequence: This is a sequence where the difference between each term is the same. For example, in the sequence ( 3, 6, 9, 12, \ldots ), we add 3 each time (this is called the common difference).
Geometric Sequence: In this type, you find each term by multiplying the previous term by a certain number. For example, in the sequence ( 2, 6, 18, 54, \ldots ), you multiply by 3 each time (this is called the common ratio).
It's important to understand sequences because they help us learn about series later on. Series are just the sums of the terms in a sequence!