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:
[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]
