Answer:
7.50
Step-by-step explanation:
The n th term of a geometric series is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
5[tex](\frac{1}{3}) ^{n-1}[/tex] is the n th term of a geometric series
with a = 5 and r = [tex]\frac{1}{3}[/tex]
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(1-r^{n}) }{1-r}[/tex], thus
[tex]S_{10}[/tex] = [tex]\frac{5(1-((\frac{1}{3}) ^{10}) }{1-\frac{1}{3} }[/tex]
= [tex]\frac{5(1-\frac{1}{59049}) }{\frac{2}{3} }[/tex]
= [tex]\frac{5(\frac{59048}{59049}) }{\frac{2}{3} }[/tex]
= [tex]\frac{15}{2}[/tex] × 0.9999..
= 7.5 × 0.9999...
≈ 7.50 ( to the nearest hundredth )
