Answer:
The 9th term of the sequence is:
Step-by-step explanation:
Given the sequence
1, 4/3,16/9
computing the ratios of all the adjacent terms
[tex]\frac{\frac{4}{3}}{1}=\frac{4}{3},\:\quad \frac{\frac{16}{9}}{\frac{4}{3}}=\frac{4}{3}[/tex]
The difference between all the adjacent terms is the same and equal to
[tex]r=\frac{4}{3}[/tex]
A geometric sequence has a constant ratio 'r' and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
As
so substituting [tex]a_1=1[/tex] and [tex]r=\frac{4}{3}[/tex] in the nth term of the equation
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=\left(\frac{4}{3}\right)^{n-1}[/tex]
Now, substitute n = 9 to determine the 9th term
[tex]a_9=\left(\frac{4}{3}\right)^{9-1}[/tex]
[tex]a_9=\left(\frac{4}{3}\right)^8[/tex]
[tex]a_9=\frac{4^8}{3^8}[/tex]
[tex]a_9=\frac{65536}{6561}[/tex]
Therefore, the 9th term of the sequence is:
