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.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.