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Mathematics Essentials 11
Patterns and Relations
7. Model real-world problems using functions, equations, inequalities and discrete structures
7.9 Geometric series
Geometric Series Formula and Sum
Discover the geometric series formula, learn how to sum a finite geometric series, and practice with clear worked examples.
What You'll Learn
A geometric series is the sum of the terms of a geometric sequence, where each term is found by multiplying the previous one by a fixed common ratio.
The sum of the first n terms is given by the formula S sub n equals a sub 1 times the quantity 1 minus r to the n, all divided by 1 minus r, for r not equal to 1.
The formula comes from multiplying the series by the common ratio and subtracting to cancel out the repeating middle terms.
Geometric series can be written compactly using sigma notation, and when the common ratio is between negative 1 and 1 the series can also be summed to infinity.
What You'll Practice
1
Finding sums of geometric series given the first 12 terms
2
Calculating series sums when given first and last terms without knowing n
3
Solving multi-step word problems with bouncing objects and percentage heights
4
Determining common ratios from series with positive and negative terms
Why This Matters
Geometric series are essential for modeling real-world situations involving exponential growth and decay, from calculating loan payments and investment returns to analyzing physics problems like bouncing balls. This skill is foundational for calculus, finance, and scientific applications.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Practice exercises
Learning resources
Skills
Geometric Series
Common Ratio
Series Formula
Sequences vs Series
Word Problems
Exponential Patterns
Percentage Applications
NS Curriculum Aligned