Identify the sequence graphed below and the average rate of change from n = 1 to n = 3. coordinate plane showing the point 2, 8, point 3, 4, point 4, 2, and point 5, 1.
answer choices:
an = 8(1/2)^n − 2; average rate of change is −6
an = 10(1/2)^n − 2; average rate of change is 6
an = 8(1/2)^n − 2; average rate of change is 6
an = 10(1/2)^n − 2; average rate of change is −6

Let  be the n'the term of the sequence.

The first term of the sequence is

the second is 8

the third term  is 4

the fourth term is 2

the fifth  term is 1

We notice that:

i) the values of the terms are powers of 2, and decreasing:



ii) we also notice that the subscript integer of a, and the power of 2 at that term, add  to 5.

thus the general term of the sequence is given by:
              
                                                  .

to fit the choices of the question, we can modify this formula as follows:



The average rate of change from n=1 to n=3 is defined as:



can be found using the general formula, 

,

thus the average rate of change is  (4-16)/2=-12/2=-6

 ,

 average rate of change=-6

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