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MariettaO [177]
3 years ago
5

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
Mathematics
1 answer:
Alik [6]3 years ago
3 0

Let a_n be the n'the term of the sequence.


The first term of the sequence is a_1

the second a_2 is 8

the third term  a_3 is 4

the fourth term a_4 is 2

the fifth  term a_5 is 1


We notice that:

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

a_2=8=2^3\\\\a_3=4=2^2\\\\a_4=2=2^1\\\\a_5=1=2^0\\\\.\\\\.

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:
              
                                                  a_n=2^{(5-n)}.

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

a_n=2^{(5-n)}=2^{3-(n-2)}=2^3\cdot2^{-(n-2)}=8\cdot (\frac{1}{2})^{(n-2)}


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

\frac{a_3-a_1}{3-1}= \frac{a_3-a_1}{2}


a_1 can be found using the general formula, 

a_1=2^{(5-1)}=2^{4}=16,

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



Answer:

 a_n=8\cdot (\frac{1}{2})^{(n-2)},

 average rate of change=-6


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