Answer:
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:
[tex]x_n=a+d(n-1)[/tex]
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:
[tex]x_n=-56-3(n-1)[/tex]
The 99th term is when n = 99. Thus:
[tex]x_{99}=-56-3(99-1)[/tex]
Evaluate:
[tex]x_{99}=-56-3(98)=-56-294=-350[/tex]
Our answer is B.
