Arithmetic Sequences
Concept
A progression is a sequence of numbers that follow a specific pattern. An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. In an arithmetic progression, there is a possibility to derive a formula for the nth term.
We can define an arithmetic progression in two ways:
i. An arithmetic progression is a sequence where the differences between every two consecutive terms are the same.
ii. An arithmetic progression is a sequence where each term, except the first term, is obtained by adding a fixed number to its previous term.
Rules
In an arithmetic sequence, each term is found by adding the same number to the previous term.
To write an algebraic expression describing the arithmetic sequence, determine the greatest common factor between each term in the sequence.
Example
Write the next 3 terms in the sequence.
5, 8, 11, 14, _____, _____, ______.
Solution
1. Each term in the pattern increases by 3.
2. Add 3 to the last term and the next two terms.
Answer: 17, 20, 23
Practice Arithmetic Sequences
Practice Problem 1
Write an algebraic expression to find any term in the sequence.
Write ‘n’ for the variable.
6, 12, 18, 24, …
Practice Problem 2
Select the algebraic expression that could be used to find any term in the sequence.
7, 11, 15, 19, __, __, __
What is the 9th term in the sequence?
Practice Problem 3
The table below shows the price of apples depending on quantity.
Select an algebraic expression that represents the given situation.
What is the price of 2kg of apples?
Algebraic Expression – an expression that contains variables, numbers, and at least one operation.
Term – each number in a sequence.
Arithmetic Sequence – each term is found by multiplying the same number to the previous term.
Geometric Sequence – each term is found by adding the same number to the previous term.
Common Difference – the number that a sequence is increased or decreased by.