Interesting question. Good to know for computer science.
Suppose you have a function like
an = 3x - 2 Try the first couple
a1 = 3(1) - 2
a1 = 3 - 2
a1 = 1
a2 = 3(2) - 2
a2 = 6 - 2
a2 = 4 So each term differs by 3
a2 - a1 = 3
an = a_(n - 1) + 3
a3 = a2 + 3
a3 = 4 + 3
a3 = 7
a4 = a3 + 3
a4 = 7 + 3
a4 = 10
a5 = a4+ 3
a5 = 10 + 3
a5 = 13
I'll do one more and then check it.
a6 = a5 + 3
a6 = 13 + 3
a6 = 16
a6 = 3x -2
a6 = 3*6 - 2
a6 = 18 - 2
a6 = 16 which checks.
So the general formula is
an = a_(n - 1) * k if you were multiplying or
an = a_(n - 1) + k if you were adding. The key thing is that you are working with the previous term.
ANSWER
EXPLANATION
First we need to find the equation of the boundary line which passes through (-1,-3) with a y-intercept of -5.
The slope of this line is
The equation of this line is
Since the boundary line is solid and the upper half plane is shaded the required inequality is
Add -27 to 6
to get your answer make sure to actually put the negative signs and you'll get the answer
