Question

find the average rate of change between n=2 and n=6?

Answer 1

Well in this case the rate of change is constant all along which makes it easier. but in the general case you take the ratio between the change in the output \((y)\) and change in input \((x)\) between your two points.
In our case we have value of 14 at n=2. so we can say \(x = 2 \implies y = 14\)
We have value of 2 at n=6. so we can say \(x = 6 \implies y = 6\).
So now we can calculate the change between the values of the two points:
$$
\Delta y = 2 - 14 = -12 \\
\Delta x = 6 - 2 = 4 \\
\text{average_rate_of_change} = \frac{\Delta y}{\Delta x} = \frac{-12}{4} = -3
$$