Skip to content

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

Related Documents

Was this page helpful?