Answered

Which of these sequences is a geometric sequence?



1, 2, 4, 7, 11, 16, 22, …




2, 4, 8, 14, 22, 38, …




3, 6, 9, 12, 15, 18, 21, …




3, 9, 27, 81, 343, 729, …



NextReset

Verified Answer :

nobillionaireNobley

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

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

 

Related Questions