Which function describes the arithmetic sequence shown?

1,7, 13, 19, 25, 31, ...

A)

f (x) = 6x + 5

B)

f (x) = 5x + 6

C)

f (x) = 5x - 6

D)

f (x) = 6% - 5

f (x) = 6x-5

Step-by-step explanation:

The common difference is 6 because of the following:

7-1=6

13-7=6

19-13=6

25-19=6

31-25=6

The common difference is the slope of the linear equation.

Slope-intercept form for a function is f (x) = mx+b where m is the slope and b is the y-intercept.

We just found m=6.

f (x) = 6x+b

The y-intercept happens at x=0.

I'm referring to looking at the data as:

x | y

1 | 1

2| 7

3| 13

4| 19

5| 25

6| 31

We can use the pattern that y goes up by 6 as x goes up by 1 to find what happens at x=0.

x| y

0 1-6=-5

So b=-5.

So the function that we are looking for is f (x) = 6x-5.