Answer:
[tex]a_n=-7+4(n-1)[/tex]
or
[tex]a_n=-7+(n-1)(4)[/tex]
Step-by-step explanation:
-7,-3,1,5,... is a arithmetic sequence.
Arithmetic sequences have a common difference. That is, it is going up by 4 each time.
When you see arithmetic sequence, you should think linear equation.
The point-slope form of a line is [tex]y-y_1=m(x-x_1)[/tex].
m is the common difference, the slope.
Any they are using the point at x=1 in the point slope form. So they are using (1,-7).
So let's put this into our point-slope form:
[tex]y-(-7)=4(x-1)[/tex]
[tex]y+7=4(x-1)[/tex]
Subtract 7 on both sides:
[tex]y=-7+4(x-1)[/tex]
So your answer is
[tex]a_n=-7+4(n-1)[/tex]
