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Recurrence Relations
High School
Definition
A recurrence relation defines sequence terms using previous terms. It's essential for analyzing recursive algorithm complexity.
Formulas
aₙ = a_n-1 + a_n-2
Fibonacci recurrence
T(n) = 2T(n/2) + n
Merge sort recurrence
aₙ = r · a_n-1 ⇒ aₙ = a₁ · r^n-1
Geometric sequence
Examples
Example 1
If a₁ = 1, aₙ = 2aₙ₋₁ + 1, find the first 5 terms.
Applications
Algorithm Analysis
Time complexity
Dynamic Programming
Optimization problems
Finance
Compound interest
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