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Mathematics Essentials 11
Patterns and Relations
7. Model real-world problems using functions, equations, inequalities and discrete structures
7.8 Geometric sequences
Geometric Sequences and the Geometric Sequence Formula
Understand what a geometric sequence is, learn the formula for the nth term, and practice with worked examples of the common ratio.
What You'll Learn
A geometric sequence is a list of numbers where each term is found by multiplying the previous term by a fixed common ratio.
The explicit formula for the nth term is a sub n equals a sub 1 times r to the power of n minus 1.
The recursive formula defines each term from the one before it: a sub n equals a sub n minus 1 times r.
The common ratio r is found by dividing any term by the term right before it.
Geometric sequences grow or shrink exponentially, unlike arithmetic sequences which change by a constant difference.
What You'll Practice
1
Verifying geometric sequences by calculating ratios between consecutive terms
2
Finding specific terms using the geometric sequence formula
3
Determining which term has a given value through trial and error
4
Solving systems of equations to find T1 and r from two known terms
5
Working with algebraic expressions to find common ratios and term values
Why This Matters
Geometric sequences model exponential growth and decay in real life, from compound interest and population growth to radioactive decay. Mastering this topic prepares you for advanced algebra, calculus, and applications in finance, science, and engineering.
Before You Start — Make Sure You Can:
This Unit Includes
5 Video lessons
Practice exercises
Learning resources
Skills
Geometric Sequences
Common Ratio
Exponential Patterns
Sequence Formulas
Algebraic Substitution
Systems of Equations
NS Curriculum Aligned