ANSWER
[tex]S_5=91\frac{10}{81}[/tex]
EXPLANATION
The sum of the first [tex]n[/tex] terms of a geometric sequence is given by;
[tex]S_n=\frac{a_1(1-r^n)}{1-r} ,-1<\:r<\:1[/tex]
Where [tex]n[/tex], is the number of terms and [tex]a_1[/tex] is the first term.
When [tex]n=5[/tex], we have [tex]a_1=81[/tex], we get;
[tex]S_5=\frac{81(1-(\frac{1}{9})^5)}{1-\frac{1}{9}}[/tex]
[tex]S_5=\frac{81(1-\frac{1}{59049})}{1-\frac{1}{9}}[/tex]
[tex]S_5=\frac{81(\frac{59048}{59049})}{\frac{8}{9}}[/tex]
[tex]S_5=\frac{7381}{81}[/tex]
[tex]S_5=91\frac{10}{81}[/tex]
