Finite Differences

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Finite Differences
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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.
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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.
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Example

• Find the function that gives the following
  sequence.
• 3, 11, 31, 69, 131.

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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.
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Sum of an Arithmetic Progression
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Sum of a Geometric Progression
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Example

• Find the sum of the following