Section 11.3: Sequences

11.3 Outline

1. Sequences or Progressions
2. Arithmetic sequences
   1. define sequence
   2. definition
   3. general term
3. Geometric sequences
   1. definition
   2. general term
4. Fibonacci-type sequences
   1. definition
   2. general term
5. 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 ms₁ and s₂ are given.  The Fibonacci sequence is that sequence for which s₁ = s₂ = 1.