B) -350
Step-by-step explanation:
We are given the sequence:
-56, -59, -62, -65...
And we want to determine its 99th term.
First, note that we have an arithmetic sequence. This is because each subsequent term differs from the previous term by a common difference.
In this case, each subsequent term is 3 less than the previous term, so our common difference d is -3.
To find the 99th term, we can write an explicit formula. The explicit formula for an arithmetic sequence is:
![x_n=a+d(n-1)](/tpl/images/2293/7458/32789.png)
Where x_n represents the nth term, a is the initial term, and d is the common difference.
Since the first term is -56, a = -56.
By substitution, we acquire:
![x_n=-56-3(n-1)](/tpl/images/2293/7458/eb9db.png)
The 99th term is when n = 99. Thus:
![x_{99}=-56-3(99-1)](/tpl/images/2293/7458/a224f.png)
Evaluate:
![x_{99}=-56-3(98)=-56-294=-350](/tpl/images/2293/7458/17c95.png)
Our answer is B.