Question

if a geometric sequence has a common ratio greater than one, the sequence exhibits growth.

Explanation:

Step1: Recall Geometric Sequence Growth

A geometric sequence is of the form \( a_n = a_1 r^{n - 1} \), where \( a_1 \) is the first term and \( r \) is the common ratio. If \( r>1 \) and \( a_1>0 \), each term is larger than the previous (e.g., \( 2, 4, 8, 16, \dots \) with \( r = 2 \)). This is exponential growth because the term value increases multiplicatively by a factor greater than 1, following an exponential pattern.

Step2: Confirm the Term

The key term for growth in a geometric sequence with \( r > 1 \) (and positive initial term) is "exponential" as the growth is characterized by the exponential function form of the sequence.

Answer:

exponential