Respuesta :
Answer:
[tex]a_n=-3(3)^{n-1}[/tex] ; {-3,-9, -27,- 81, -243, ...}
[tex]a_n=-3(-3)^{n-1}[/tex] ; {-3, 9,-27, 81, -243, ...}
[tex]a_n=3(\frac{1}{2})^{n-1}[/tex] ; {3, 1.5, 0.75, 0.375, 0.1875, ...}
[tex]a_n=243(\frac{1}{3})^{n-1}[/tex] ; {243, 81, 27, 9, 3, ...}
Step-by-step explanation:
The first explicit equation is
[tex]a_n=-3(3)^{n-1}[/tex]
At n=1,
[tex]a_1=-3(3)^{1-1}=-3[/tex]
At n=2,
[tex]a_2=-3(3)^{2-1}=-9[/tex]
At n=3,
[tex]a_3=-3(3)^{3-1}=-27[/tex]
Therefore, the geometric sequence is {-3,-9, -27,- 81, -243, ...}.
The second explicit equation is
[tex]a_n=-3(-3)^{n-1}[/tex]
At n=1,
[tex]a_1=-3(-3)^{1-1}=-3[/tex]
At n=2,
[tex]a_2=-3(-3)^{2-1}=9[/tex]
At n=3,
[tex]a_3=-3(-3)^{3-1}=-27[/tex]
Therefore, the geometric sequence is {-3, 9,-27, 81, -243, ...}.
The third explicit equation is
[tex]a_n=3(\frac{1}{2})^{n-1}[/tex]
At n=1,
[tex]a_1=3(\frac{1}{2})^{1-1}=3[/tex]
At n=2,
[tex]a_2=3(\frac{1}{2})^{2-1}=1.5[/tex]
At n=3,
[tex]a_3=3(\frac{1}{2})^{3-1}=0.75[/tex]
Therefore, the geometric sequence is {3, 1.5, 0.75, 0.375, 0.1875, ...}.
The fourth explicit equation is
[tex]a_n=243(\frac{1}{3})^{n-1}[/tex]
At n=1,
[tex]a_1=243(\frac{1}{3})^{1-1}=243[/tex]
At n=2,
[tex]a_2=243(\frac{1}{3})^{2-1}=81[/tex]
At n=3,
[tex]a_3=243(\frac{1}{3})^{3-1}=27[/tex]
Therefore, the geometric sequence is {243, 81, 27, 9, 3, ...}.
