Question

Find the common ratio for the following geometric sequence 2, 1, 0.5, 0.25

Answer 1

X 0.5 is the common ratio

Answer 2

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

$a(1)=2,~~a(2)=1,~~a(3)=0.5,~~a(4)=0.25,~~.~~.~~.$

So, we get

$\dfrac{a(2)}{a(1)}=\dfrac{1}{2}=0.5,\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{0.5}{1}=0.5,\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{0.25}{0.5}=0.5,~etc.$

Thus, the required common ratio for the given geometric sequence is 0.5.

Option (C) is CORRECT.