8/3. Option B is correct
The given sequence 9, 6, 4... is a geometric sequence. The nth term of the geometric sequence is expressed as:
[tex]T_n=ar^{n-1}[/tex]where:
a is the first term
n is the number of terms
r is the common ratio
From the sequence;
a = 9
r = 6/9 = 4/6 = 2/3
n = 4 (we need the 4th term)
Substitute the given parameters into the formula
[tex]\begin{gathered} T_4=9(\frac{2}{3})^{4-1} \\ T_4=9(\frac{2}{3})^3 \\ T_4=\cancel{9}(\frac{8}{\cancel{27}^3}) \\ T_4=\frac{8}{3} \end{gathered}[/tex]Hence the next term of the sequence is 8/3
