Answer
The sequence is neither arithmetic nor geometric.
Work Step by Step
$\bf\text{RECALL:}$
$\bf\text{(1) Arithmetic Sequence }$
A sequence is arithmetic if there exists a common difference $d$ among consecutive terms.
$d=a_n-a_{n-1}$
The sum of the first $n$ terms of an arithmetic sequence is given by the formulas:
$S_n=\frac{n}{2}(a_1 +a_n)$
or
$S_n=\frac{n}{2}\left(2 a_1 + (n-1)d\right)$
$\bf\text{(2) Geometric Sequence }$
A sequence is geometric if there exists a common ratio $r$ among consecutive terms.
$r=\dfrac{a_n}{a_{n-1}}$
The sum of the first $n$ terms of a geometric sequence is given by the formula:
$S_{n}=a_1 \cdot \dfrac{1-r^n}{1-r}$
In the formulas listed above,
$d$ = common difference
$r$ = common ratio
$a_1$ = first term
$a_n$ = nth term
$n$ = number of terms
$\bf\text{Identify the sequence as arithmetic or geometric.}$
The sequence has $a_1$. $a_2=3$, $a_3=6$.
$a_2-a_1 = 3-1=2
\\a_3-a_2=6-3=3$
There is no common difference, so the sequence is not arithmetic.
$\dfrac{a_2}{a_1} = \dfrac{3}{1}=3
\\\dfrac{a_3}{a_2} = \dfrac{6}{2}=2$
There is no common ratio, so the sequence is not geometric.
