Answer:
a(n) = 216 + 0.5^(n - 1) and a(n) = 216 - 0.5^(n - 1)
Step-by-step explanation:
The formula for the nth element of a geometric sequence is a(n) = a(1) * q^(n - 1).
[tex]a_3=a_1q^2=54\\a_9=a_1q^8=\frac{27}{32}\\\\\texttt{Divide the second equation by the first}\\\\\frac{a_1q^8}{a_1q^2}=\frac{\frac{27}{32}}{54}\\\\q^6=\frac1{64}\\\\q=\pm \frac12\\\\\texttt{Substitute for }q\texttt{ in the first equation and solve for }a_1\\\\a_1(\pm 0.5)^2=54\\\frac{a_1}4=54\\a_1 =216[/tex]
Therefore, the geometric sequences are a(n) = 216 + 0.5^(n - 1) and a(n) = 216 - 0.5^(n - 1)