Question

PLEASE HELP ME WITH THIS QUESTION!!! 20 PTS. PLZZ.

Answer 1

The appropriate descriptors of geometric sequences are ...

... B) Geometric sequences have a common ratio between terms.

... D) Geometric sequences are restricted to the domain of natural numbers.

_____

The sequences may increase, decrease, or alternate between increasing and decreasing.

If the first term is zero, then all terms are zero—not a very interesting sequence. Since division by zero is undefined, the common ration of such a sequence would be undefined.

There are some sequences that have a common difference between particular pairs of terms. However, a sequence that has the same difference between all adjacent pairs of terms is called an arithmetic sequence, not a geometric sequence.

Any sequence has terms numbered by the counting numbers: term 1, term 2, term 3, and so on. Hence the domain is those natural numbers. The relation describing a geometric sequence is an exponential relation. It can be evaluated for values of the independent variable that are not natural numbers, but now we're talking exponential function, not geometric sequence.