Answer
The sequence is neither geometric nor arithmetic.
Work Step by Step
In order to determine if the sequence is geometric, we see if the quotient of all consecutive terms is constant.
Here, we have:
$\dfrac{a_{2}}{a_1}=\dfrac{9}{8}$ and $\dfrac{a_{3}}{a_2}=\dfrac{16}{15}$
This shows that the quotient of all consecutive terms is not constant. Thus, it is not a geometric sequence.
In order to determine if the sequence is arithmetic, we see if the difference of all consecutive terms is constant.
Here, we have:
$a_2-a_1=\dfrac{1}{12}$ and $a_3-a_2=\dfrac{1}{20}$
This shows that the difference of all consecutive terms is not constant. Thus, it is not an arithmetic sequence.
Hence, the sequence is neither geometric nor arithmetic.
