Please see my work shown below to fill in your boxes.
Answer: (8,1)
Step-by-step explanation:
The line that connects (-4,5) and (2,3) has a slope of (-2/6) or -1/3. The y-intercept is calculated from one of the points: 3 = -(1/3)*(2) + b
b = 3 2/3
The equation for the line is y = -(1/3)x + 3 2/3
The reflection covers a distance of x of (2 - (-4)) = 6. Add 6 to the x value of (2,3) and calculate the resulting y. (8,y): y = -(1/3)(8) + 3 2/3, y = -8/3 + 11/3 = 3/3 or 1
The point is (8,1)
The explicit rule is an = a1 + 12 * (n - 1).
From the recursive rule, we can tell that each term is 12 more than the previous term, so we can write a1 + 12 * n.
However, if that's the rule, then when a1 is plugged in, it doesn't work. So, we must do 12 * (n - 1) to make it work.
Therefore, the explicit rule is:
an = a1 + 12 * (n - 1).