Geometric Sequence

Category: Algebra Date: November 19, 2024 Quickbytes ID: 003-255-533

What is a Geometric Sequence?

A geometric sequence is a list of numbers where each number is found by multiplying the previous one by the same number. For example, in 2, 4, 8, 16, each number is multiplied by 2.

General Form of a Geometric Sequence

A geometric sequence can be written as: a, \, ar, \, ar^2, \, ar^3, \, \dots

where:

  • a is the first term of the sequence,
  • r is the common ratio, and
  • each term is obtained by multiplying the previous term by r.

For example, in the sequence 2, 6, 18, 54, \dots, the first term is a = 2, and the common ratio is r = 3 because each term is multiplied by 3 to get the next term.

Real-World Applications of Geometric Sequences

  1. Finance:
    • Compound interest calculations involve geometric sequences.
    • Example: If you invest 100 at an annual interest rate of 10%, the amount after n years is a geometric sequence: 100, 110, 121, 133.1, \dots.
  2. Science:
    • Modeling population growth, radioactive decay, and spread of diseases, which follow geometric patterns.
  3. Technology:
    • Signal strength in communication systems often decreases geometrically with distance.
Geometric Sequences – Nerdstudy
What are the formulas for arithmetic and geometric sequences