Question

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

Which of the following are true statements about geometric sequences?
There is more than one correct answer. Select all that apply.

(MORE THAN ONE ANSWER)

A) Geometric sequences only increase, never decrease.
B) Geometric sequences have a common ratio between terms.
C) Geometric sequences can have a first term of 0.
D) Geometric sequences are restricted to the domain of natural numbers.
E) Geometric sequences have a common difference between terms.

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.