Mathematics
Grade 9
15 min
Arithmetic sequences
Arithmetic sequences
What you'll learn
- Estimate the length of common classroom objects (e.g., pencil, textbook) to the nearest centimeter or millimeter with at least 75% accuracy.
- Identify the most appropriate metric unit (millimeter, centimeter, meter, kilometer, milliliter, liter, gram, kilogram) for measuring a given object or quantity with 80% accuracy.
- Convert between common metric units (e.g., meters to centimeters, liters to milliliters) within the same system of measurement with at least 70% accuracy.
- Explain the relationship between different metric units (e.g., how many centimeters are in a meter) using mathematical reasoning and appropriate vocabulary.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define an arithmetic sequence and identify its key components.
Determine the common difference of an arithmetic sequence.
Write the explicit formula for the nth term of an arithmetic sequence.
Use the explicit formula to find the value of any term in a sequence.
Find the number of terms in a finite arithmetic sequence.
Model and solve real-world problems using arithmetic sequences.
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This tutorial introduces arithmetic sequences, which are ordered lists of numbers with a constant difference. You will learn how to identify these patterns, write a formula to describe them, and use that formula to make predictions. This is a key buildi...
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Key Concepts & Vocabulary
TermDefinitionExample
SequenceAn ordered list of numbers, often following a specific pattern or rule.2, 4, 6, 8, 10, ...
TermEach individual number in a sequence. We use subscript notation like a₁, a₂, a₃ to denote the first, second, and third terms.In the sequence 5, 10, 15, 20, the third term (a₃) is 15.
Arithmetic SequenceA sequence in which the difference between any two consecutive terms is constant.3, 7, 11, 15, 19, ... (The difference is always 4).
First Term (a₁)The very first number in a sequence.In the sequence 10, 8, 6, 4, ..., the first term (a₁) is 10.
Common Difference (d)The constant value that is added to each term to get the next term in an arithmetic sequence. It can be positive or negative.In the sequence 50, 45, 40, 35, ..., the common difference (d) is -5.
nth Term (a...
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Core Formulas
Finding the Common Difference
d = a_n - a_{n-1}
To find the common difference (d), subtract any term from the term that immediately follows it. For example, d = a₂ - a₁ or d = a₅ - a₄.
The Explicit Formula for an Arithmetic Sequence
a_n = a_1 + (n - 1)d
This is the most important formula for arithmetic sequences. It allows you to find the value of any term (aₙ) if you know the first term (a₁), the position of the term you want (n), and the common difference (d).
4 more steps in this tutorial
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Challenging
Three consecutive terms of an arithmetic sequence are given by the expressions x + 2, 3x - 1, and 4x. What is the value of x?
A.2
B.5
C.3
D.4
Challenging
The sum of the 2nd and 5th terms of an arithmetic sequence is 23. The 8th term is 29. What is the explicit formula for the sequence?
A.a_n = 4n - 5
B.a_n = 3n + 2
C.a_n = 5n - 6
D.a_n = 4n - 3
Challenging
An arithmetic sequence has a first term of 60 and a common difference of -7. What is the term number (n) of the first negative term in this sequence?
A.10th term
B.9th term
C.8th term
D.11th term
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Frequently asked questions
What grade level is "Arithmetic sequences"?
Arithmetic sequences is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Arithmetic sequences?
You'll be able to: Estimate the length of common classroom objects (e.g., pencil, textbook) to the nearest centimeter or millimeter with at least 75% accuracy; Identify the most appropriate metric unit (millimeter, centimeter, meter, kilometer….
Is "Arithmetic sequences" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Arithmetic sequences?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.