Question

Find the 99th term of the

Answer 1

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:

$x_n=a+d(n-1)$

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:

$x_n=-56-3(n-1)$

The 99th term is when n = 99. Thus:

$x_{99}=-56-3(99-1)$

Evaluate:

$x_{99}=-56-3(98)=-56-294=-350$

Our answer is B.