Answer
The sequence is arithmetic.
Common difference: $d=-\frac{3}{5}$.
General term: $a_{n}=-\frac{3}{5}n+\frac{43}{5}$
Work Step by Step
$\frac{37}{5}-8=\frac{34}{5}-\frac{37}{5}=\frac{31}{5}-\frac{34}{5}=\frac{28}{5}-\frac{31}{5}=5-\frac{28}{5}=-\frac{3}{5}$
We see that the difference between each term and the preceding term is same and is equal to $-\frac{3}{5}$.
Therefore, the sequence is arithmetic with common difference $d=-\frac{3}{5}$.
The general term $a_{n}$ is given by
$a_{n}=a_{1}+(n-1)d$
As $a_1=8$ and $d=-\frac{3}{5}$, we have:
$\implies a_{n}=8+(n-1)(-\frac{3}{5})=8-\frac{3}{5}n+\frac{3}{5}$
Or $a_{n}=-\frac{3}{5}n+\frac{43}{5}$
