Mathematics
Grade 9
15 min
Skip-counting sequences
Skip-counting sequences
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1
Introduction & Learning Objectives
Learning Objectives
Identify a sequence as arithmetic, geometric, or neither.
Determine the common difference (d) or common ratio (r) of a sequence.
Write the explicit formula for the nth term of an arithmetic or geometric sequence.
Use the explicit formula to calculate any term in a sequence.
Model real-world scenarios using skip-counting sequences.
Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.
Ever wonder how a viral video's views explode or how your savings could grow over time? 📈 These patterns are just advanced forms of skip-counting!
In this tutorial, we'll level up your understanding of skip-counting by exploring two powerful types of sequences: arithmetic and geometric. You'll learn how to describe...
2
Key Concepts & Vocabulary
TermDefinitionExample
SequenceAn ordered list of numbers, where each number is called a term. The order is determined by a specific rule or pattern.The list 5, 10, 15, 20, 25, ... is a sequence.
Term (a_n)An individual number in a sequence. The notation a_n refers to the term in the nth position (e.g., a_1 is the first term, a_5 is the fifth term).In the sequence 5, 10, 15, 20, ..., the third term, a_3, is 15.
Arithmetic SequenceA sequence where you add or subtract the same constant number to get from one term to the next. This is like skip-counting by addition.The sequence 4, 1, -2, -5, ... is an arithmetic sequence because you subtract 3 each time.
Common Difference (d)The constant number that is added to each term to get the next term in an arithmetic sequence.In the sequence 4, 1, -2,...
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Core Formulas
Explicit Formula for an Arithmetic Sequence
a_n = a_1 + (n-1)d
Use this formula to find any term (a_n) in an arithmetic sequence when you know the first term (a_1), the common difference (d), and the term number (n) you want to find.
Explicit Formula for a Geometric Sequence
a_n = a_1 \cdot r^{(n-1)}
Use this formula to find any term (a_n) in a geometric sequence when you know the first term (a_1), the common ratio (r), and the term number (n) you want to find.
4 more steps in this tutorial
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Challenging
In an arithmetic sequence, the 3rd term is 14 and the 8th term is 34. What is the explicit formula for this sequence?
A.a_n = 6 + (n-1)4
B.a_n = 14 + (n-1)4
C.a_n = 4 + (n-1)6
D.a_n = 10 + (n-1)4
Challenging
In a geometric sequence, the 2nd term is 12 and the 5th term is 96. What is the 8th term?
A.384
B.576
C.768
D.1536
Challenging
Which exponential function g(n) = a * b^n correctly models the geometric sequence 4, 12, 36, ... where n is the term number (n=1, 2, 3...)?
A.g(n) = 4 * 3^n
B.g(n) = 4/3 * 3^n
C.g(n) = 4 * 3^(n-1)
D.g(n) = 3 * 4^(n-1)
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