Question

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, …


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Answer 1

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 :

`(A)/(AR)=(AR)/(AR^2)=(AR^2)/(AR^3)=......=(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}=(9)/(3)=(27)/(9)=(81)/(27)=(343)/(81)=(729)/(343)=3`

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

Answer 2

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