Sequences
Arithmetic and geometric sequences
Learning Objectives
Discussion Starters
Differentiation Ideas
Presentation Mode
lessons (3)
1
Introduction to Sequences
Learn what sequences are, how to identify patterns, and write rules for finding any term.
Advanced25 minTeacher View
2
Arithmetic Sequences
Learn to identify, analyze, and work with arithmetic sequences where terms increase or decrease by a constant difference.
Advanced25 minTeacher View
3
Geometric Sequences
Learn about sequences where each term is multiplied by a constant ratio to get the next term.
Advanced25 minTeacher View
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 Students Will 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 $S = \frac{a_1}{1-r}$.