Answer:
Option A is correct that is [tex]1,\frac{1}{2},\frac{1}{4}[/tex]
Step-by-step explanation:
We have been given a formula [tex]a_n=\frac{1}{2}\cdot a_n-1[/tex]
[tex]a_1=1[/tex]
We will put values of n in [tex]a_n=\frac{1}{2}\cdot a_n-1[/tex]
when n=2 we get
[tex]a_2=\frac{1}{2}\cdot a_2-1[/tex]
[tex]\Rightarrow a_2=\frac{1}{2}\cdot a_1[/tex]
[tex]\Rightarrow a_2=\frac{1}{2}\cdot 1[/tex]
[tex]\Rightarrow a_2=\frac{1}{2}[/tex]
when n=3
[tex]a_3=\frac{1}{2}\cdot a_2[/tex]
[tex]\Rightarrow a_3=\frac{1}{2}\cdot \frac{1}{2}[/tex]
[tex]\Rightarrow a_3=\frac{1}{4}[/tex]
Therefore, Option A is correct that is [tex]1,\frac{1}{2},\frac{1}{4}[/tex]
