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Which sequence is modeled by the graph below? points are (1,3) (2,0.6) (3, 0.12)
A an = 3 (one fifth )^n − 1
B an = 3(−5)^n − 1
C an = 0.3(5)^n − 1
D an = one fifth (3)^n − 1

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ANSWER
[tex]a_n =3( \frac{1}{5} ) ^{n - 1} [/tex]
Step-by-step explanation

The ordered points given to us are
[tex](1,3),(2,0.6),(3,0.12)[/tex]
The y-coordinates are the terms in the sequence.

We use the y-coordinates to determine the common ratio.

[tex]r = \frac{0.6}{3} = \frac{0.12}{0.6} = \frac{1}{5} [/tex]

The first term of the sequence is the first y-coordinate.

[tex]a_1 = 3[/tex]

The nth term of an exponential sequence is given by,



[tex]a_n =a_1 \times r ^{n - 1} [/tex]


We now substitute the above values in to the general formula to obtain,


[tex]a_n =3( \frac{1}{5} ) ^{n - 1} [/tex]

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