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Sequence and Series

Sequence and Series. Ch. 4.7-4.9. Sequence: A set of numbers with a pattern (each number is called a term) Each term is separated by a comma Domain of a sequence is the set of consecutive integers The set of numbers is the output

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Sequence and Series

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  1. Sequence and Series Ch. 4.7-4.9

  2. Sequence: • A set of numbers with a pattern (each number is called a term) • Each term is separated by a comma • Domain of a sequence is the set of consecutive integers • The set of numbers is the output • These are found by plugging the numbers into a rule or equation

  3. Series • A sum of numbers with a pattern (each number is called a term) • Each term is separated by a + sign • Domain (INPUT) is set by the summation notation or is estimated to be the first n consecutive integers • The OUTPUT is usually one single number or the string of numbers added • Summation Notation: • The domain of the summation is listed on the top and bottom of the sigma • Top = end number (input) • Bottom = start number (input) • Function to find each term to be added for the summation

  4. Sequences and Series can be defined as either Arithmetic or Geometric • Arithmetic – has a common difference (d) (add or subtract the same number) • ALWAYS LINEAR • Example: -3,1,5,9….. • Geometric – has a common ratio ( r ) or multiplier for each term • ALWAYS EXPONENTIAL • Example: 2,8,32,128….

  5. How can we quickly find the sum of a longer summation: • Example: Use this formula:

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