Sequences
Arithmetic and geometric sequences
Start with the basics and progress through 3 lessons. Each lesson builds on the previous one.
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Test Your Knowledge
10 questions, new mix each time (from 51)
In This Topic (3 lessons)
Introduction to Sequences
Learn what sequences are, how to identify patterns, and write rules for finding any term.
Arithmetic Sequences
Learn to identify, analyze, and work with arithmetic sequences where terms increase or decrease by a constant difference.
Geometric Sequences
Learn about sequences where each term is multiplied by a constant ratio to get the next term.
Sequences are ordered lists of numbers following patterns; series are sums of sequences. Understanding arithmetic and geometric sequences, along with their sum formulas, is essential for financial mathematics and calculus.
What You'll Learn
- Identify arithmetic and geometric sequences
- Find the nth term of a sequence
- Calculate sums of arithmetic series
- Calculate sums of geometric series
- Apply sequences to real-world problems
Frequently Asked Questions
What is the difference between arithmetic and geometric sequences?
Arithmetic: add a constant difference. Geometric: multiply by a constant ratio.
What is the sum formula for arithmetic series?
$S_n = \frac{n}{2}(a_1 + a_n)$
Can a geometric series sum to infinity?
If |r| < 1, the infinite geometric series converges to $S = \frac{a_1}{1-r}$.