Question

do we get a GP if each term is multiplied or divided by a constant?

Answer 1

Yes. In a geometric progression, the RATIOS of adjacent terms must be constant. A ratio does not change if the numerator & denominator are multiplied or divided by a constant.
If you don't believe me, check for yourself:
Take this G.P:
a,ar^2,ar^3.....
Now multiply each term by a constant k:
ak,ar^2k,ar^3k...
Is the ratio of the adjacent terms constant here?

Answer 2

thx