Question

WILL MEDAL AND FAN
Identify the sequence graphed below and the average rate of change from n = 0 to n = 2.
http://gyazo.com/77dcb86a2ddf5bc616de00d52dbcd1a0

Answer 1

an=20(1/2)^n-1; average rate of change is 15/2
an=10(1/2)^n-1; average rate of change is 15/2
an=20(1/2)^n-1; average rate of change is 15/2
an=10(1/2)^n-1; average rate of change is -15/2

They have the same option for the first and third choices but I think the third choice is supposed to be -15/2

Answer 2

Makes sense that the 3rd choice should be -15/2. As for picking the correct sequence, you can just check the points. For \(20(\frac{1}{2})^{n-1}\), if you plug in n = 1, you'd have
\(20(\frac{1}{2})^{0} = 20\)
So clearly that is incorrect and the correct sequence would have to be \(10(\frac{1}{2})^{n-1}\).

Now, notice your points are decreasing as x gets larger. So this would represent a negative slope, so the average rate of change would have to be negative, giving the last option as your answer.

If you were not given the possible choices for the average rate of change, you would simply find the slope between the coordinate points at n = 0 and n = 2.

If we plug in n = 0 into the sequence, we get \(10(\frac{1}{2})^{-1} = 10(2) = 20\)
Thus we have the point (0,20). Taking this point and point (2,5), we can find the rate of change between these two points, which is simply the same as finding the slope. I assume you recall the formula for slope
\[\frac{ y_{2} - y_{1} }{ x_{2} - x_{1} } = slope\]

Now of course your answer choices made it obvious, but this would be the idea if you needed to get it yourself.

Answer 3

Thank you so much! :)

Answer 4

No problem :)