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)
*can only be found when a geometric sequence where |r|<1
ReplyDeleteFormula: S = t1/1-r
*if |r| is not less than 1 we say the series diveges - doesn't approach a #
* if |r|<1 then we say the series approaches a #
Example:
1. Find the sum of the infinite series: 9 - 6 + 4
(geometric)
r = -6/9 = -2
|-2/3| < 1
S = 9/(1 - (-2/3)) = 27/5