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

`(a(2))/(a(1))=(1)/(2)=0.5,\\\\\\(a(3))/(a(2))=(0.5)/(1)=0.5,\\\\\\(a(4))/(a(3))=(0.25)/(0.5)=0.5,~etc.`

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

Option (C) is CORRECT.