Answer
The sequence is neither geometric nor arithmetic.
Work Step by Step
For the sequence to be geometric, the quotient of all consecutive terms must be constant.
Here, we have:
$\dfrac{a_{2}}{a_1}=\dfrac{1/5}{-1/3}$ and $\dfrac{a_{3}}{a_2}=\dfrac{3/7}{1/5}$
This shows that the quotient of all consecutive terms is not constant and thus it is not a geometric sequence.
In order for the sequence to be arithmetic, the difference of all consecutive terms must be constant.
Here, we have: $a_2-a_1= \dfrac{3}{7}-\dfrac{1}{5} \ne a_3-a_2=\dfrac{1}{5}-\dfrac{-1}{3}$
This shows that the difference of all consecutive terms is not constant and thus it is not an arithmetic sequence.
Hence, the sequence is neither geometric nor arithmetic.
