(Note): Hello! I am really stuck on this problem and am trying to figure out how to solve it! I don't want the answer, I just want to know how to solve an equation like this:
Consider a sequence whose first five terms are: -1.75, -0.5, 0.75, 2, 3.25
Which function (with domain all integers n ≥ 1) could be used to define and continue this sequence?
A. f(n) = 7/4(n - 1) - 5/4
B. f(n) = 5/4(n - 1) - 7/4
C. f(n) = 7/4n - 5/4
D. f(n) = 5/4n - 7/4
Any help is appreciated! Thanks in advance!
each term is 1.25 more than the last, so the slope is 5/4
That means only B,D are possible.
Now plug in n=4 and see which formula correctly gives the value 2
Thank you oobleck! I got B, so I'm gonna go with that!
To solve this problem, we need to identify the pattern in the given sequence and use that pattern to determine the correct function.
Let's analyze the given sequence:
Term 1: -1.75
Term 2: -0.5
Term 3: 0.75
Term 4: 2
Term 5: 3.25
Looking at the terms, we can observe that each term is found by adding 1.25 to the previous term. So, in general, the nth term can be found by adding (n - 1) * 1.25 to the first term.
Now, let's check the options provided:
A. f(n) = 7/4(n - 1) - 5/4
B. f(n) = 5/4(n - 1) - 7/4
C. f(n) = 7/4n - 5/4
D. f(n) = 5/4n - 7/4
Comparing the options to our general rule of (n - 1) * 1.25, we can see that option D matches the pattern:
f(n) = 5/4n - 7/4
Therefore, the correct function that could be used to define and continue this sequence is option D.
To solve this problem, you need to find the function that generates the given sequence. Here's how you can approach it:
Step 1: Look for a pattern in the sequence.
The given sequence is: -1.75, -0.5, 0.75, 2, 3.25
Let's consider the difference between consecutive terms:
-1.75 - (-0.5) = -1.25
-0.5 - 0.75 = -1.25
0.75 - 2 = -1.25
2 - 3.25 = -1.25
We notice that the difference between consecutive terms is constant, and it's -1.25 in this case.
Step 2: Express the nth term of the sequence using the constant difference.
The first term is -1.75.
The constant difference is -1.25.
To find the nth term of the sequence, we can use the formula:
nth term = first term + (n - 1) * constant difference
Applying this formula, we get:
nth term = -1.75 + (n - 1) * (-1.25)
= -1.75 - 1.25n + 1.25
Simplifying, we have:
nth term = -1.75 + 1.25 - 1.25n
= -0.5 - 1.25n
Step 3: Compare the expression with the given options.
We have the expression: -0.5 - 1.25n
Comparing it with the given options:
A. f(n) = 7/4(n - 1) - 5/4
B. f(n) = 5/4(n - 1) - 7/4
C. f(n) = 7/4n - 5/4
D. f(n) = 5/4n - 7/4
We can see that the correct option is:
D. f(n) = 5/4n - 7/4
So, the function that could be used to define and continue this sequence is f(n) = 5/4n - 7/4.