Help with recognizing a geometric sequence

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trivialaxxf · Accepted Answer

That lies in its very definition: there is a common ratio between successive terms of the geometric sequence. That is to say, a number is being multiplied to get each successive term, and this "number" is nothing but the common ratio. This means that you just have to check if there is a number being multiplied between successive terms.
If you also think about it, the common ratio is what you get when you divide a term by its predecessor. But you can probably already tell why you get the same number - it is because you have been multiplying the same number.
The "common ratio" can be anything, but it has been widely argued without a proper consensus that a sequence with a common ratio 0 or 1 should not be called geometric. But thinking about that argument is futile, as you would never, ever encounter a sequence such as that in questions. Even if you do, you can think for yourself.
Here are three examples:
1.

1, 2, 4, 8, \dots

- the common ratio is 2.
2.

- 1, 3, - 9, 27

- the common ratio is -3.
3.

7, 1, \frac{1}{7}, \frac{1}{49}

- the common ratio is 1/7.

Help with recognizing a geometric sequence

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