Answer
$a_{1}=-3, a_{2}=-4,a_{n}=a_{n-2}+a_{n-1}$
The next three terms are $-29,-47$ and $-76$.
Work Step by Step
There is no common difference. So, the sequence is not arithmetic.
There is no common ratio. So, the sequence is not geometric.
Let's look for a pattern. We note that
$a_{1}+a_{2}=(-3)+(-4)=-7=a_{3}$
$a_{2}+a_{3}=(-4)+(-7)=-11=a_{4}$ and so on.
Beginning with the third term, each term is the sum of the previous two terms.
So, a recursive rule for the sequence is
$a_{1}=-3, a_{2}=-4,a_{n}=a_{n-2}+a_{n-1}$
The next three terms are:
$a_{6}=a_{4}+a_{5}=(-11)+(-18)=-29$
$a_{7}=a_{5}+a_{6}=(-18)+(-29)=-47$
$a_{8}=a_{6}+a_{7}=(-29)+(-47)=-76$
