Identify if each sequence is arithmetic, geometric, or neither.
$7,10,16,25,37,\dots$

• A. Arithmetic
• B. Geometric
• C. Neither

Answer: (C)

Verified step by step guidance

1. First, recall the definitions: an arithmetic sequence has a constant difference between consecutive terms, and a geometric sequence has a constant ratio between consecutive terms.
2. Calculate the differences between consecutive terms: \$10 - 7 = 3\(, \)16 - 10 = 6\(, \)25 - 16 = 9\(, and \)37 - 25 = 12$. Since these differences are not the same, the sequence is not arithmetic.
3. Next, calculate the ratios between consecutive terms: \(\frac{10}{7}\), \(\frac{16}{10}\), \(\frac{25}{16}\), and \(\frac{37}{25}\). Since these ratios are not constant, the sequence is not geometric.
4. Since the sequence is neither arithmetic nor geometric, it falls into the category of neither.
5. Therefore, the sequence does not have a constant difference or ratio, confirming it is neither arithmetic nor geometric.