Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.

y = 20*(1/2)^(n-1)

average rate of change = -7.5

Step-by-step explanation:

In the graph, the point (1, 20) is missing.

This kind of plot in which every value of the function is a half of the previous one (10, 5, 2.5, 1.25) has the next form: y = a*(1/2)^(n-1). From here is deduced that for n = 1, y = 20, so that, for the next n-value (2), y = 20/2 = 10.  

Replacing n = 1  in the formula gives:

y = a*(1/2)^(1-1)

y = a = 20

So,  y = 20*(1/2)^(n-1)

The average rate of change from n = 1 to n = 3 is calculated taking into account y-values at those n-values, as follows:

average rate of change = (y3 - y1)/(n3 - n1) =  (5 - 20)/(3 - 1) = -7.5

It coincides with the slope of the line which intercepts those points.