Answer: The correct option is (C) 0.5.
Step-by-step explanation: We are given to find the common ratio for the following geometric sequence :
2, 1, 0.5, 0.25, . . .
We know that
in a geometric sequence, the ratio of any term to its preceding term is the required common ratio of the sequence.
In the given sequence <a(n)>, we have
[tex]a(1)=2,~~a(2)=1,~~a(3)=0.5,~~a(4)=0.25,~~.~~.~~.[/tex]
So, we get
[tex]\dfrac{a(2)}{a(1)}=\dfrac{1}{2}=0.5,\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{0.5}{1}=0.5,\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{0.25}{0.5}=0.5,~etc.[/tex]
Thus, the required common ratio for the given geometric sequence is 0.5.
Option (C) is CORRECT.
