If you are good at sequences in math please help I am giving more points

C. 101 - 5(n - 1)

Step-by-step explanation:

d = (26 - 71)/(16 - 7)

d = -45/9

d = -5

a7 = a1 + (7-1)(-5)

71 = a1 - 30

a1 = 101

an = 101 + (n - 1)(-5)

an = 101 - 5(n - 1)

C. is the answer.

Step-by-step explanation:

Arithmetic sequences are linear.

So their slope is the same no matter the two points you choose.

We are given the following two points:

(7,71)

(16,26)

We can find the slope by subtracting vertically here and putting y difference on top of x difference.

71-26=45

7-16=-9

The slope is 45/-9=-5.

The equation so far is

a(n)=-5n+b

To find b we will use a known point on the line like (7,71):

71=-5(7)+b

71=-35+b

Add 35 on both sides:

106=b

The equation for the nth term is

a(n)=-5n+106

Now you could expand your choices to see switch matches.

Or you could write this equation into the form presented in the choices.

a(n)=-5(n-1+1)+106

a(n)=-5(n-1)-5+106

a(n)=-5(n-1)+101

Or

a(n)=101-5(n-1)

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: