Question

What is the common ratio of the geometric sequence 1, 4, 16, 64, ...?

Answer 1

4/1=16/4=64/16=4 is the common ratio

Answer 2

The common ratio of the geometric sequence 1, 4, 16, 64, . . . is 4

Given :

The geometric sequence 1, 4, 16, 64, . . .

To find :

The common ratio of the geometric sequence

Solution :

Step 1 of 2 :

Write down the given sequence

Here the given geometric sequence is

1, 4, 16, 64, . . .

First term = 1

Second term = 4

Step 2 of 2 :

Find the common ratio of the geometric sequence

For a given geometric sequence the common ratio is obtained by dividing any term in the sequence by the previous term

Hence the required common ratio of the geometric sequence

$\displaystyle \sf{ = \frac{Second \: term}{First \: term} }$

$\displaystyle \sf{ = \frac{4}{1} }$

$\displaystyle \sf{ = 4 }$

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