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Geometric sequences

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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


What You'll Learn

Identify geometric sequences by finding the common ratio between consecutive terms
Apply the formula Tn = T1 × r^(n-1) to find any term in a geometric sequence
Calculate the common ratio by dividing any term by its preceding term
Determine unknown terms or positions using algebraic manipulation of the general formula
Solve for first terms and common ratios when given non-consecutive terms

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

Skills

Geometric Sequences
Common Ratio
Exponential Patterns
Sequence Formulas
Algebraic Substitution
Systems of Equations
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