Answer
The $n^{th}$ term of the geometric sequence is: $a_n=-1 (-2)^{n-1}$
and $a_{10}= 512$
Work Step by Step
The $n^{th}$ term of the sequence is given by the formula:
$ a_n=a_1r^{n-1}$
where $r$=common ratio and $a_1$= the first term
The common ratio of a geometric sequence is equal to the quotient of any term and the term before it:
$ \ r = \dfrac{a_n}{a_{n-1}}$ or, $r=\dfrac{a_2}{a_1}=\dfrac{2}{-1}=-2$
Therefore, the $n^{th}$ term of the geometric sequence is: $a_n=-1 (-2)^{n-1}$
Now, the 10th term can be computed by substituting $10$ for $n$:
$a_{10}=-1 (-2)^{10-1}=-1 \cdot (-512)= 512$
