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Sequences and Series (Important terms (Arithemtic (Adding or Subtracting),…
Sequences and Series
Important terms
Arithemtic
Adding or Subtracting
Geometric
Multiplying or dividing
Series
Adding up all numbers in a given sequence
Sequence
a set of numbers that are found using a given rule (arithmetic or Geometric)
Common difference
What you add or subtract by when looking at an arithmetic sequence
Common ratio
What you multiply or divide by when looking at a Geometric sequence
Formulas
Explicit formula (arithmetic)
d= common difference; U1= the first term
Explicit formula (Geometric)
r=the common ratio; U1= first term
Sum formulas for finite arithmetic series
Sum formula for finite Geometric Series
Examples
Geometric sequence
5,20,80,320...
multiply by 4 each time
Arithmetic sequence
3,6,9,12....
add by 3 each time
Finite Sequence
3,6,9,12,15,18
6 terms
Example problem
