MATH 10 1stquar

• Arithmetic sequence

  Also known as arithmetic progression
• Arithmetic sequence


  • Has a common number that is added to get the next term
  • The common number is found by subtracting the previous term from the current term
• Common difference


  The fixed number that is added to get the next term in an arithmetic sequence
• a1, a2, a3, a4


  The first, second, third, fourth terms in an arithmetic sequence
• Arithmetic mean


  The average found between two extremes in an arithmetic sequence
• Finding arithmetic mean


  1. Add the two extremes and divide by 2

  2. Use the formula: (a1 + an)/2
• 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
• Finite sequence


  Domain is positive integers with a last term
• Infinite sequence


  Domain is positive integers without a last term
• Deriving general term


  1. Substitute values into formula

  2. Check if formula matches first few terms
• Alternating sign sequences use (-1)^n in general term
• Sequence: is a function whose domain is the set of positive integers it is also means an ordered list of numbers.
• Arithmetic Sequence: A sequence where every term is obtained by adding a fixed number to its predecessor, this common difference is denoted as d.
• Geometric Sequences: A sequence where every term is obtained by multiplying the previous term by a constant called the common ratio r.