Does the sequence18 , 14, 12 ,1… is it a geometric sequence?

We know that a sequence is geometric if it has the same common ratio between each term. And the common ratio is the number we multiply by a number and get the next number of the sequence.Let the common ratio be r and we will take the ratio asSecond TermFirst term , Third TermSecond term For the first two terms, we should have 18×r=14 For the second and third terms, we should have 14×r=12Let us calculate the common ratio in each case. For the first two terms 18, 14 The ratio will be taken as Second TermFirst term . That is 1/41/8 = 42=2.So the ratio becomes r = 2As we can see, the common ratio is the same. So, we can say that the given sequence is the geometric sequence.

Does the sequence18 , 14, 12 ,1… is it a geometric sequence?

We know that a sequence is geometric if it has the same common ratio between each term. And the common ratio is the number we multiply by a number and get the next number of the sequence.Let the common ratio be r and we will take the ratio asSecond TermFirst term , Third TermSecond term For the first two terms, we should have 18×r=14 For the second and third terms, we should have 14×r=12Let us calculate the common ratio in each case. For the first two terms 18, 14 The ratio will be taken as Second TermFirst term . That is 1/41/8 = 42=2.So the ratio becomes r = 2As we can see, the common ratio is the same. So, we can say that the given sequence is the geometric sequence.

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Does the sequence $\frac{1}{8}$ , $\frac{1}{4},$ $\frac{1}{2}$ ,1… is it a geometric sequence?

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Detailed Solution

We know that a sequence is geometric if it has the same common ratio between each term. And the common ratio is the number we multiply by a number and get the next number of the sequence.
Let the common ratio be r and we will take the ratio as