in a geometric sequence, the generator is the number that one term is multiplied by to generate the next term.

Well, for example, your common ratio (generator) could be 0.5, which is less than 1, but greater than 0. Let us look at what happens with different starting values.

**80**: 80, 40, 20, 10, 5, 2.5, 1.25, .625, .3125, ....

**200: **200, 100, 50, 25, 12.5, 6.25, 3.125, ...

**1024: **1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, .5, .25, .125, ...

We can pick any number of examples with different starting values and different common ratios between 0 and 1, but the idea is that in each case, the numbers would always get smaller (since we are multiplying by a number less than 1), but never change sign from positive to negative (since we are multiplying by a positive number), so **
our terms would get closer and closer to zero, but never reach it.**