Respuesta :

semsee45

Answer:

[tex]a_n=100 \left(\dfrac15\right)^{n-1}[/tex]

Step-by-step explanation:

General equation of geometric sequence:  [tex]a_n=ar^{n-1}[/tex]

Given:

  • a₁ = 100
  • a₂ = 20
  • a₃ = 4

[tex]\implies a_1=a=100[/tex]

[tex]\implies a_2=100 \cdot r=20[/tex]

[tex]\implies a_3=100 \cdot r^2=4[/tex]

Common ratio:

[tex]r=\dfrac{a_3}{a_2}=\dfrac{4}{20}=\dfrac15[/tex]

Therefore:

[tex]a_n=100 \left(\dfrac15\right)^{n-1}[/tex]