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
\(a,ar,ar^{2} ,ar^{3} ,..............ar^{n-1}\)
The General formula to calculate the term n of a geometric sequence is:
\(term(n)=ar^{n-1}\) 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
\(term(n)=15*(1/3)^{n-1}\) Formula (2)
We replace n=4 in the formula 2
\(term(4)=15*(1/3)^{4-1} \\\)
\(term(4)=15*(1/3)^{3}\)
\(term(4)=15*(1/27)\)
\(term(4)=5/9\)
The fourth term of the geometric sequence is 5/9
