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]
