the first 5 terms of a linear sequence are given below: 8,6,4,2,0...
What is the 100th term in the sequence?
A. -192
B. -190
C. -108
D. -90
I could figure this out in like 5 minutes, but I know there's a pattern I can't remember to figure it out quicker.
term(n) for an arithmetic sequence is (a+(n-1)d )
your a=8, d=-2 , n=100
term(100) = a + 99d
= 8 + 99(-2) = -190
Ah, linear sequences, how predictable they can be! Let's see if we can use some clown logic to figure this out, shall we?
Now, we start with 8 and keep decreasing by 2 each time. If we calculate how many times 2 goes into 8, we get 4. And if we multiply 4 by 2, we get 8! Coincidence? I think not!
So, if we continue this pattern, we can determine that 2 goes into 100 fifty times. And if we take our initial term, which is 8, and subtract 2 fifty times, what do we get? Drumroll, please...
(-2 * 50) + 8 = -100 + 8 = -92! But wait! That's not any of the options given; seems like a clownish plot twist!
But don't fret, my friend, we're not done yet. We need to remember that our initial term is 8. So, if we subtract 8 from our previous result, which is -92, what do we get?
-92 - 8 = -100! Huzzah! That's option B, -190, in case you were wondering.
So, my final answer is B. -190. Don't worry if you didn't get it in 5 minutes; clowns always take the scenic route to the punchline!
To find the pattern and determine the 100th term in the sequence, we need to identify the common difference between consecutive terms.
From the given sequence, we can observe that each term is decreasing by 2.
Starting with the first term, 8, we can calculate the nth term of the sequence using the formula:
nth term = first term + (n - 1) * common difference
For the 100th term, n is equal to 100. Let's substitute these values into the formula:
100th term = 8 + (100 - 1) * (-2)
= 8 + 99 * (-2)
= 8 - 198
= -190
Therefore, the 100th term in the sequence is -190.
So, the correct answer is option B: -190.
To find the 100th term in the given sequence, you first need to identify the pattern of the sequence. In this case, you can observe that each term in the sequence is decreasing by 2. The common difference between the terms is -2.
To find the nth term of a linear sequence, you can use the formula: an = a1 + (n - 1)d, where an represents the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
In this case, a1 = 8 (as given in the question), n = 100 (since we are looking for the 100th term), and d = -2 (the common difference).
Plugging these values into the formula, we have:
a100 = 8 + (100 - 1)(-2)
= 8 + 99(-2)
= 8 - 198
= -190.
Therefore, the 100th term in the sequence is -190.
So, option B: -190 is the correct answer.