Question

Which of these sequences is a geometric sequence?

Answer 1

3, 9, 27, 81, 343, 729, … is a geometric sequence because each term is obtained by multiplying 3 to the preceding term.

Answer 2

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:

  $A, AR, AR^2,AR^3,AR^4,........$

Ratio of two consecutive terms is :

   $\frac{A}{AR}=\frac{AR}{AR^2}=\frac{AR^2}{AR^3}=......=\frac{1}{R}$

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

$\text{Common Ratio}=\frac{9}{3}=\frac{27}{9}=\frac{81}{27}=\frac{343}{81}=\frac{729}{343}=3$

Option D : 3, 9, 27, 81, 343, 729, …..is a geometric sequence