Answer:
a=1, b=1/3, c=1/27
Step-by-step explanation:
The table is given below:
[tex]\left|\begin{array}{c|c}$Powers of 3&Value\\----&---\\3^3&27\\3^2&9\\3^1&3\\3^0&a\\3^{-1}&b\\3^{-2}&\frac{1}{9} \\3^{-3}&c\end{array}\right|[/tex]
(a)As the exponents decrease, the next term is gotten by a division of the previous term by 3.
[tex]f_n=f_{n-1}\div 3[/tex]
(b)
[tex]f_n=f_{n-1}\div 3\\I.a=f_n, f_{n-1}=3,\\a=f_n=3\div 3=1\\II. b=f_n, f_{n-1}=1,\\b=f_n=1\div 3=\frac{1}{3}\\III. c=f_n, f_{n-1}=\frac{1}{9},\\c=f_n=\frac{1}{9}\div 3=\frac{1}{27}[/tex]
a=1, b=1/3, c=1/27
