Answer:
C. is the answer.
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)
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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)