Respuesta :

gmany

Answer:

[tex]\large\boxed{a_n=6\left(\dfrac{1}{10}\right)^{n-1}}[/tex]

Step-by-step explanation:

Check:

[tex]n=1\\\\a_1=6\left(\dfrac{1}{10}\right)^{1-1}=6\left(\dfrac{1}{10}\right)^0=6(1)=6\qquad\bold{CORRECT}\ (1,\ 6)\\\\n=2\\\\a_2=6\left(\dfrac{1}{10}\right)^{2-1}=6\left(\dfrac{1}{10}\right)^1=6\left(\dfrac{1}{10}\right)=\dfrac{6}{10}=0.6\qquad\bold{CORRECT}\ (2,\ 0.6)\\\\n=3\\\\a_3=6\left(\dfrac{1}{10}\right)^{3-1}=6\left(\dfrac{1}{10}\right)^2=6\left(\dfrac{1}{100}\right)=\dfrac{6}{100}=0.06\qquad\bold{CORRECT}\ (3,\ 0.06)[/tex]

isyllus

Answer:

[tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]

Option 3 is correct

Step-by-step explanation:

The coordinates are (1,6) (2,0.6) and (3,0.06)

If we make table of given coordinate:

x   :    1          2         3  

y   :   6        0.6     0.06

[tex]a_1=6,a_2=0.6,a_3=0.06[/tex]

Ratio of the sequence:

[tex]r=\dfrac{a_2}{a_1}=\dfrac{0.6}{6}=0.1[/tex]

Formula of geometric sequence:

[tex]a_n=ar^{n-1}[/tex]

[tex]a_n=6\cdot 0.1^{n-1}[/tex]

[tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]

Hence, The sequence model by [tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]

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