Question

which explains why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve?

• the range contains only natural numbers.
• the domain contains only natural numbers.
• exponential bases must be whole numbers.
• initial values must be whole numbers.

Explanation:

Define the domain of a sequence

A sequence is a function whose domain is restricted to discrete values, specifically the set of natural numbers \(n \in \{1, 2, 3, \dots\}\) representing the term positions.

Analyze the graphical representation

Because the input values (domain) are discrete integers rather than continuous real numbers, the graph consists only of isolated points \((n, a_n)\) corresponding to each term, rather than a continuous, smooth curve.

Answer:

• The range contains only natural numbers.
• The domain contains only natural numbers. (Correct answer)
• Exponential bases must be whole numbers.
• Initial values must be whole numbers.