11.3 Outline

A.  Sequences or Progressions
B. Arithmetic sequences
      1. define sequence
      2. definition
      3. general term
C. Geometric sequences
      1. definition
      2. general term
D.  Fibonacci-type sequences
      1. definition
      2. general term
E.  Procedure for classifying sequences

11.3 Essential Ideas

An arithmetic sequence is a sequence whose consecutive terms differ by the same real number, called the common difference.  The general term of an arithmetic sequence a₁, a_2, a_3, ... a_n, with common difference d is a_n = a₁ + (n - 1)d.

A geometric sequence is a sequence whose consecutive terms have the same quotient, called the common ratio.  The general term of a geometric sequence g₁, g_2, g_3, ... g_n, with common ratio r is g_n = g₁r^n-1.

A Fibonacci-type sequence is a sequence in which the general term is given by the formula s₁ = s_n-1 + s_n-2 where s₁ and s₂ are given.  The Fibonacci sequence is that sequence for which s₁ = s₂ = 1.