Answer
neither
Work Step by Step
$a_1=\frac{-1}{3},a_2=\frac{1}{5},a_3=\frac{3}{7}$
In order for a sequence to be geometric, the quotient of all consecutive terms must be constant.
Hence here: $\frac{\frac{3}{7}}{\frac{1}{5}}\ne\frac{\frac{1}{5}}{-\frac{1}{3}}$, which is not constant thus it is not a geometric sequence.
In order for a sequence to be arithmetic, the difference of all consecutive terms must be constant.
Hence here: $\frac{3}{7}-\frac{1}{5}\ne\frac{1}{5}-\frac{-1}{3}$, which is not constant thus it is not an arithmetic sequence.
Hence it is neither.
