Answer with Explanation:
A Sequence is said to be geometric sequence ,if the ratio of two consecutive terms is same.For example,
Look at the sequence:
[tex]A, AR, AR^2,AR^3,AR^4,........[/tex]
Ratio of two consecutive terms is :
[tex]\frac{A}{AR}=\frac{AR}{AR^2}=\frac{AR^2}{AR^3}=......=\frac{1}{R}[/tex]
The ratio of any term to the term Preceding it is called Common ratio. Here Common ratio is =R,which will be same for the entire Sequence.
Now, looking at the option Carefully
In option D
[tex]\text{Common Ratio}=\frac{9}{3}=\frac{27}{9}=\frac{81}{27}=\frac{343}{81}=\frac{729}{343}=3[/tex]
Option D : 3, 9, 27, 81, 343, 729, …..is a geometric sequence
