Math Sequences
Fascinating patterns of sequences through interactive visual simulations
Essential Formulas
Arithmetic Sequence
aₙ = a₁ + (n-1)dSum of Arithmetic Sequence
Sₙ = n/2 × (a₁ + aₙ)Geometric Sequence
aₙ = a₁ × r^(n-1)Sum of Geometric Sequence
Sₙ = a₁(1-r^n)/(1-r) for r≠1Interactive Visualizations
Explore different types of sequences by adjusting parameters and watching how the pattern evolves. Visualize how changing the first term, common difference, or common ratio affects the sequence.
Sequence Generator
Pattern Explanation:
Sequence Pattern Explorer
What comes next?
2, 4, 6, 8, 10, ...?
3, 6, 12, 24, ...?
1, 4, 9, 16, ...?
Find the pattern rule
3, 8, 13, 18, 23, ...
2, 6, 18, 54, ...
Test Your Knowledge
Question 1 of 3
What is the 5th term in the arithmetic sequence with a₁ = 3 and d = 4?
Real-world Applications
Financial Mathematics
Geometric sequences model compound interest and financial growth over time. Each term represents the amount after a specific time period.
Computer Algorithms
Sequences help analyze algorithm efficiency and determine how processing time increases with input size.
Natural Patterns
The Fibonacci sequence appears in nature, from flower petals and pinecones to the spiral arrangement of seeds.