Answer:
[tex]\frac{15}{2}[/tex]
Step-by-step explanation:
The problem has a mistake, it should NOT be 2 = 5, rather a=5.
Now, given a = 5 (the first term is a), and
r = 1/3 (common ratio),
we can solve for the sum of the infinite series by using the formula:
[tex]S_{\infty}=\frac{a}{1-r}[/tex]
Where [tex]S_{\infty}[/tex] is the sum of the infinite geometric series,
a is the first term (given as 5), and
r is the common ratio ( r= 1/3 given)
We now plug these into the formula and get our answer:
[tex]S_{\infty}=\frac{a}{1-r}\\=\frac{5}{1-\frac{1}{3}}\\=\frac{5}{\frac{2}{3}}\\=\frac{15}{2}[/tex]
