a geometric sequence is a bunch of numbers where you can get from a number to the next number by multiplying the previous number by a certain number
might be confusing so here's an example
1,2,4,8,16
each term is multiplied by 2 to get next term, that number that each term is multiplied by is called the common ratio
formula for geometric sequence is
[tex]a_n=a_1(r)^{n-1}[/tex]
where [tex]a_n[/tex] is nth term
[tex]a_1[/tex] is first term
r is teh common ratio
n=which term
in our example
1,3, 9, 27, 81
each term is being multiplied by 3 so it is a geometric sequence and thus r=3
also first term is 1 so [tex]a_1=1[/tex]
so the formula is [tex]a_n=1(3)^{n-1}[/tex] or in function notation [tex]f(n)=1(3)^{n-1}[/tex]
This is a geometric sequence.
from 1-3 one is multiplied by three
from 3-9 three is multiplied by three
from 9-27 nine is multiplied by three
and from 27-81 27 is multiplied by three
Hope this helped!!
|Sophia M|
