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A Guide to Finite Differences Method for Sequence Formulas

Learn how to find explicit formulas for sequences not in common progressions using finite differences method. Solve equations and explore sigma notation. Example included.

jeffreybrewer
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A Guide to Finite Differences Method for Sequence Formulas

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  1. Finite Differences

  2. Finite Differences If the sequence does not fall into an arithmetic or Geometric progression you can use Finite Differences to find the Explicit Formula. 12 20 28 36 44 8 8 8 8 Stop! Equation is 2nd degree.

  3. Now we will create 3 equations: Plug 1, 2 and 3 in for x (1, 2, 3 stands for the term number) Now solve 3 equations with 3 variables.

  4. Example Find the function that gives the following sequence. 3, 11, 31, 69, 131….

  5. Sigma Notation Sigma Notation is a notation used to abbreviate long summations of a given expression . Where n is the upper boundary and m is the lower boundary.

  6. Sum of an Arithmetic Progression:

  7. Sum of a Geometric Progression

  8. Example Find the sum of the following:

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