Which description best distinguishes arithmetic from geometric sequences?

• A. Arithmetic uses addition of a constant; geometric uses multiplication by a constant
• B. Arithmetic uses multiplication; geometric uses addition
• C. Both are defined by division
• D. They are the same type of sequence

Answer: (D)

The key idea is how each step to the next term is formed. An arithmetic sequence adds a fixed amount each time, while a geometric sequence multiplies by a fixed factor each time. For example, starting at 2 and adding 3 each time gives 2, 5, 8, 11 — arithmetic. Starting at 3 and multiplying by 2 each time gives 3, 6, 12, 24 — geometric. This difference (addition of a constant vs. multiplication by a constant) is what distinguishes them. The other descriptions don’t fit: using multiplication or division for both, or saying they’re the same type, misstate how the next term is produced.