Which description best distinguishes arithmetic from geometric sequences?

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.

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.