the first five terms of a sequence are shown below:

8,6,4,2,0 ...
What is the 100th term in the sequence?
A. -192
B. -190
C. -108
D. -90
I know how to figure this out but it would take a few minutes. There UST be some sort of formula?

Yes, there is a formula that can help you find the nth term of this sequence more efficiently. In this particular sequence, each term is decreasing by 2. So, to find the nth term, you can use the formula:

nth term = first term + (n - 1)d

Where:
- first term is the initial term of the sequence (in this case, 8),
- n is the position of the term you want to find (in this case, 100), and
- d is the common difference between terms (in this case, -2, since the terms are decreasing by 2).

Now, let's use the formula to find the 100th term:

100th term = 8 + (100 - 1)(-2)
= 8 + (99)(-2)
= 8 - 198
= -190

Therefore, the 100th term in the sequence is -190, so the correct option is B.

Yes, there is a formula to find the nth term of an arithmetic sequence. An arithmetic sequence is a sequence in which each term is obtained by adding a constant difference, called the common difference, to the previous term.

In this case, we can observe that the common difference is -2, as each term is obtained by subtracting 2 from the previous term. Therefore, the formula to find the nth term of this sequence is:

nth term = first term + (n-1) * common difference

Plugging in the values for this sequence, we have:

nth term = 8 + (n-1) * (-2)

To find the 100th term, we can substitute n = 100 into the formula:

100th term = 8 + (100-1) * (-2)
= 8 + 99*(-2)
= 8 - 198
= -190

Therefore, the 100th term in this sequence is -190, which corresponds to option B.

the first five terms of a linear sequence are 8,6,4,2,0....

What is the 100th term of the sequence?
I could figure this out with a few minutes of patience. But I know there is formula which I cannot find anymore to solve it quicker :)