# How do you find a formula of the nth term for this sequence: 8/9,1,9/8,81/64?

The nth term of the given series is ${\left(\frac{9}{8}\right)}^{n - 2}$
In the sequence: $\left\{\frac{8}{9} , 1 , \frac{9}{8} , \frac{81}{64} , \ldots \ldots \ldots\right\}$ the ratio of a term to its preceding term is $\frac{9}{8}$, Hence it is a geometric sequence.
In a geometric sequence, if $a$ is the first term and ratio of a term with its preceding term is $r$, nth term is given by $a . {r}^{n - 1}$.
Hence nth term of the given series is $\left(\frac{8}{9}\right) \cdot {\left(\frac{9}{8}\right)}^{n - 1}$ or ${\left(\frac{9}{8}\right)}^{n - 2}$