Answer
Arithmetic sequence
$a_{n}=-\frac{2}{3}n+\frac{14}{3}$
Work Step by Step
$\frac{10}{3}-4=\frac{8}{3}-\frac{10}{3}=2-\frac{8}{3}=\frac{4}{3}-2=\frac{2}{3}-\frac{4}{3}=-\frac{2}{3}$
We see that the difference between each term and the preceding term is same and is equal to $-\frac{2}{3}$.
Therefore, the sequence is arithmetic with common difference $d=-\frac{2}{3}$.
The general term $a_{n}$ is given by
$a_{n}=a_{1}+(n-1)d$
As $a_1=4$ and $d=-\frac{2}{3}$, we have:
$a_{n}=4+(n-1)(-\frac{2}{3})=4-\frac{2}{3}n+\frac{2}{3}$
$a_{n}=-\frac{2}{3}n+\frac{14}{3}$
