Mathematics
Grade 9
15 min
Use a rule to complete a number sequence
Use a rule to complete a number sequence
What you'll learn
- Identify the coordinates of an image point after a translation given the coordinates of the pre-image point and the translation vector, with 80% accuracy on a formative assessment.
- Solve for the translation vector (horizontal and vertical shift) given the coordinates of a pre-image point and its corresponding image point with 75% accuracy on a summative quiz.
- Explain, in writing, the relationship between the coordinates of a pre-image point and its image point after a translation, demonstrating understanding of horizontal and vertical shifts, as assessed by a rubric with specific criteria.
- Explain, in writing, how a translation affects the coordinates of a point and describe the relationship between the pre-image and image in terms of congruence and orientation.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify if a number sequence is arithmetic, geometric, or quadratic.
Calculate the common difference or common ratio for a given sequence.
Derive the algebraic rule (nth term formula) for linear (arithmetic) and geometric sequences.
Derive the algebraic rule (nth term formula) for quadratic sequences using the method of finite differences.
Use a derived rule to find any term in a sequence, including missing terms or future terms.
Apply sequence rules to solve word problems involving patterns.
Ever wonder how video games generate levels or how your savings grow over time? 🎮 It all comes down to predictable patterns called sequences!
This tutorial will teach you how to decode the hidden rules behind lists of numbers. You will learn to identify different...
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Key Concepts & Vocabulary
TermDefinitionExample
Number SequenceAn ordered list of numbers, called terms, that follow a specific pattern or rule.The list 2, 5, 8, 11, ... is a number sequence.
Term (a_n)A single number in a sequence. The subscript 'n' indicates the term's position (e.g., a_1 is the first term, a_5 is the fifth term).In the sequence 2, 5, 8, 11, ..., the third term (a_3) is 8.
Arithmetic SequenceA sequence where the difference between consecutive terms is constant. This constant is called the common difference (d).In 4, 9, 14, 19, ..., the common difference is 5 (9 - 4 = 5).
Geometric SequenceA sequence where the ratio between consecutive terms is constant. This constant is called the common ratio (r).In 3, 6, 12, 24, ..., the common ratio is 2 (6 / 3 = 2).
Quadratic SequenceA sequenc...
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Core Formulas
Arithmetic Sequence Rule
a_n = a_1 + (n-1)d
Use this to find the nth term (a_n) of an arithmetic sequence. You need the first term (a_1) and the common difference (d).
Geometric Sequence Rule
a_n = a_1 * r^(n-1)
Use this to find the nth term (a_n) of a geometric sequence. You need the first term (a_1) and the common ratio (r).
Quadratic Sequence Rule
a_n = An^2 + Bn + C
This is the general form for a quadratic sequence. The coefficients A, B, and C are found by analyzing the first and second differences of the sequence.
4 more steps in this tutorial
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Challenging
The first term of a geometric sequence is 81, and the fourth term is -3. What is the 6th term?
A.1/3
B.1
C.-1
D.-1/3
Challenging
The first differences of a quadratic sequence are 6, 11, 16, 21, ... The 3rd term of the original quadratic sequence is 25. What was the first term (a_1)?
A.4
B.8
C.6
D.5
Challenging
Sequence P is arithmetic: 10, 13, 16, ... Sequence Q is geometric: 3, 6, 12, ... What is the first value of n for which the nth term of Q is greater than the nth term of P?
A.n = 4
B.n = 5
C.n = 6
D.n = 7
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Frequently asked questions
What grade level is "Use a rule to complete a number sequence"?
Use a rule to complete a number sequence is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Use a rule to complete a number sequence?
You'll be able to: Identify the coordinates of an image point after a translation given the coordinates of the pre-image point and the translation vector, with 80% accuracy on a formative assessment; Solve for the translation vector (horizontal….
Is "Use a rule to complete a number sequence" 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 Use a rule to complete a number sequence?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.