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Chapter 27.3
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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