Answer:
the fourth term is 5/9
Step-by-step explanation:
a sequence is defined like this:
1, 2, 3,4…….. n
1= first term
2=second term
3= third term
n=term n of the secuence
a geometric sequence is defined as follows
[tex]a,ar,ar^{2} ,ar^{3} ,..............ar^{n-1}[/tex]
The General formula to calculate the term n of a geometric sequence is:
[tex]term(n)=ar^{n-1}[/tex] Formula (1)
We can calculate any term of the sequence by replacing the information known in the formula (1):
For this case: a=a1=15 , r=1/3
[tex]term(n)=15*(1/3)^{n-1}[/tex] Formula (2)
We replace n=4 in the formula 2
[tex]term(4)=15*(1/3)^{4-1} \\[/tex]
[tex]term(4)=15*(1/3)^{3}[/tex]
[tex]term(4)=15*(1/27)[/tex]
[tex]term(4)=5/9[/tex]
The fourth term of the geometric sequence is 5/9
