A geometric sequence is a sequence of numbers where consecutive elements have a common ratio r:
[tex]\frac{a_{n+1}}{a_n}=r[/tex]
Then, we can find the next element of the sequence by multiplying the preceding element by the common ratio r:
[tex]a_{n+1}=r\cdot a_n[/tex]
If the first element of the sequence is a₁, then:
[tex]\begin{gathered} a_2=a_1\cdot r \\ a_3=a_1r^2 \\ a_4=a_1r^3 \\ \ldots \\ a_n=a_1r^{n-1} \end{gathered}[/tex]
The given information states that a₁=8 and that the common ratio is 2/3.
Then, substitute a₁=8 and r=2/3 into the expression for the n-th term:
[tex]a_n=8\cdot\mleft(\frac{2}{3}\mright)^{n-1}[/tex]
Therefore, the sequence can be written as a function as follows:
[tex]f(n)=8\cdot\mleft(\frac{2}{3}\mright)^{n-1}[/tex]
