Mathematics

• Sequence


  An ordered list of numbers
• Sequence


  • Finite - has a last term
  • Infinite - no last term
• Term


  Each number in a sequence
• General term


  A mathematical expression or rule for generating the terms of a sequence
• Finding general term


  1. Identify pattern

  2. Substitute values into formula

  3. Verify formula matches first few terms
• General term formula


  a_n = n^2 - 3

  a_n = (-1)^n / (2n - 1)

  a_n = 5n

  a_n = n(n+1)/2
• Sequences can have terms that alternate in sign
• Even exponents in general term formula result in positive terms, odd exponents result in alternating signs
• General term formulas can represent sequences of perfect squares, cubes, fractions, etc.