Which function describes the arithmetic sequence shown?
1, 7, 13, 19, 25, 31, ...
A)
ƒ(x) = 6x + 5
B)
ƒ(x) = 5x + 6
C)
ƒ(x) = 5x − 6
D)
ƒ(x) = 6x − 5
did you check your answer?
x y(5x+6)
1 11
2 16
...
Not even close. Why not show your work? You must have been just guessing.
Note that as x changes by 1, y changes by 6. So, you need to start off with
y = 6x
So, it's either A or D.
when x=1, 6x = 6, but y(1) = 5, so D is clearly your choice.
this is my question I forgot to put the answer I think its B
What made you think it was B ?
The change between consecutive numbers is 6, so
expect to see a 6x
when x=1, 6x becomes 6 but it should be 1, so we have to subtract 5
looks like 6x - 5
To determine which function describes the arithmetic sequence, we need to find the pattern or the common difference between the terms.
Looking at the sequence:
1, 7, 13, 19, 25, 31, ...
To find the common difference, we subtract any two consecutive terms. Let's subtract 1 from 7:
7 - 1 = 6
Similarly, let's subtract 7 from 13, 13 from 19, and so on:
13 - 7 = 6
19 - 13 = 6
25 - 19 = 6
31 - 25 = 6
As we can see, the common difference between the terms is 6.
Now, let's examine the given function options:
A) ƒ(x) = 6x + 5
B) ƒ(x) = 5x + 6
C) ƒ(x) = 5x − 6
D) ƒ(x) = 6x − 5
We need to check if any of these functions produce the same arithmetic sequence with a common difference of 6.
Let's plug in some values of x and see if the function gives us the corresponding terms in the sequence:
For the first term (x = 1):
A) ƒ(1) = 6(1) + 5 = 11
B) ƒ(1) = 5(1) + 6 = 11
C) ƒ(1) = 5(1) - 6 = -1
D) ƒ(1) = 6(1) - 5 = 1
None of the options match the first term (1).
Let's try another term (x = 2):
A) ƒ(2) = 6(2) + 5 = 17
B) ƒ(2) = 5(2) + 6 = 16
C) ƒ(2) = 5(2) - 6 = 4
D) ƒ(2) = 6(2) - 5 = 7
Again, none of the options match the second term (7).
By testing more terms, we can see that none of the given options match the arithmetic sequence 1, 7, 13, 19, 25, 31, ...
Therefore, none of the options A), B), C), or D) describe the arithmetic sequence shown.