When is a sequence geometric? when each term is multiplied by the same number to get the next term when there is a common difference between terms when the sequence increases or decreases in a linear pattern when the ratios between consecutive terms are reciprocals

A geometric sequence when each term is a constant multiple (or fraction) with respect to the previous term, called the common ratio.  So the first statement is true.  Mathematically:

a(2)/a(1)=a(3)/a(2)=a(4)/a(3)=r, the constant called the common ratio.

Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number.