Sequence

• A sequence is a discrete structure used to represent an ordered list that often follow a specific pattern or rule where each number in the sequence is called a term.
• Sequence Notation:

  • Each term is denoted by: an where n is the position of the term in the sequence and called as index.
• Sequence Notation:

  • Each term is denoted by: an where n is the position of the term in the sequence and called as index.
• Applications of Sequences

  • Algorithm Analysis
  • Data Structures
  • Networking
  • Database System
  • Computer Graphics
  • Machine Learning
• Explicit Formula - this formula defines the n-th term of a sequence, denoted by an.
• Sequence Rule - A sequence often follow a rule or formula to generate a term/s. This rule
• Explicit Formula Structure: an = f(n), where f(n) is a function of n. Example: an = 2n generates a sequence 2, 4, 6, 8,…

  Solve: a5: a5 = 2(5) = 10
• Initial condition - the value of the first term in the sequence.
• Recurrence relation - an equation that define the an in terms of an-1 (the previous term), an-2 (the term before an-1), or other previous terms.
• Recursive Formula two parts:

  • Initial Condition
  • Recurrence Relation