Question

In a geometric sequence, the ratio between consecutive terms is...

Answer 1

Answer: The same or equal

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Explanation:

Consider an example like 3, 6, 12, 24, 48, ...

The ratio between consecutive terms is

• 6/3 = 2
• 12/6 = 2
• 24/12 = 2
• 48/2 = 2

Each time we divide any given term over its previous one, we get the same ratio 2. We call this the common ratio. In terms of notation, the variable r is used for the common ratio, so r = 2 in this case.

As another example, the geometric sequence 5, 50, 500, 5000, ... has r = 10 as the common ratio because we multiply each term by 10 to get the next one. Moving forward has us multiply by r, moving backward and we divide by r. The value of r cannot be zero, but it can be negative.

An example with r being negative would be something like

1, -1, 1, -1, 1, -1, ....

we just bounce back and forth between those two values. In this case, r = -1.