Sequences
A sequence is simply a list of numbers.
There are two main types of sequences:
Arithmetic - where you add or subtract
Geometric - where you multiply
(*Note: division is considered Geometric. For example: If a sequence divides by three, it is considered to be multiplied by one-third.
Formulas to find a term:
Arithmetic
tn-t'+(n-1)d
n=term #
t'=first term
d=what you add
tn=term#_in sequence
Geometric
tn=t'∙r^(n-1)
r= what you multiply by
Recursive Definitions
A recursive Definition is a formula for a sequence that involves a previous term. [a(n-1)]
an= (an-1/3)
I'm having trouble with sigma notation. if anyone can help???
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Sigma has three parts
ReplyDeleteA top number
A middle number
A bottom number
Top is called limit of summation
Middle is called the summand
Bottom is called index
Top is the address of the last number in given series
Middle is the result of the tn formula
Bottom is what number you start counting at
If the equation is arithmetic then the bottom number will be 1
If the equation is geometric then the bottom number will be 0
When asked to evaluate for a sigma problem you plug in the numbers including and between the bottom and the top numbers
So if the bottom number is one and the top number is five then you would plug in 1,2,3,4,5 for the variable of the middle equation and add the results of each plug in togethe3r to get the final answer
When asked to express then you draw the sigma sign and fill in the top middle and bottom parts