## 11.3 Outline

- Sequences or Progressions
- Arithmetic sequences
- define sequence
- definition
- general term

- Geometric sequences
- definition
- general term

- Fibonacci-type sequences
- definition
- general term

- 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 *a*_{1},*a*_{2, }*a*_{3,}… *a*_{n}, with common difference *d *is *a*_{n }= *a*_{1 }*+* (*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 *g*_{1},*g*_{2, }*g*_{3,}…*g*_{n}, with common ratio *r *is* g*_{n }= *g*_{1}*r*^{n-1}*. *

A **Fibonacci-type sequence **is a sequence in which the *general term *is given by the formula *s*_{1 }= *s*_{n-1 }*+ s*_{n-2 }where m*s*_{1 }and *s*_{2 }are given. The Fibonacci **sequence **is that sequence for which *s*_{1 }= *s*_{2 }= 1.