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

Choice A



The first term is 8 as this is the y coordinate of the point when x = 1. 
The second term is 4 (since y = 4 when x = 2)
etc etc

The sequence of terms is: 8, 4, 2, 1, ...

Each time we're dividing by 2, or multiplying by 1/2. This is why r = 1/2

Put this together and we have this geometric nth term formula
an = 8*(1/2)^(n-1)

This means the answer could be A or it could be C. However, we can rule out choice C because the rate of change is not positive. Draw a line through (1,8) and (3,2) and you'll see this line has a negative slope. So the rate of change is negative.

The only answer left is choice A.

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