This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Alright KIMBE — let's do this. To determine if a sequence is arithmetic, we check if the difference between consecutive terms is constant. This constant difference is called the common difference, d. a) 3, 8, 13, 18, 23, ... Step 1: Calculate the differences between consecutive terms. 8 - 3 = 5 13 - 8 = 5 18 - 13 = 5 23 - 18 = 5 Since the difference is constant, this is an arithmetic sequence. Answer: Arithmetic, d = 5 b) 100, 94, 88, 82, ... Step 1: Calculate the differences between consecutive terms. 94 - 100 = -6 88 - 94 = -6 82 - 88 = -6 Since the difference is constant, this is an arithmetic sequence. Answer: Arithmetic, d = -6 c) 2, 4, 8, 16, 32, ... Step 1: Calculate the differences between consecutive terms. 4 - 2 = 2 8 - 4 = 4 16 - 8 = 8 Since the differences are not constant (2 ≠ 4), this is not an arithmetic sequence. Answer: Not arithmetic d) 6, 6, 6, 6, ... Step 1: Calculate the differences between consecutive terms. 6 - 6 = 0 6 - 6 = 0 6 - 6 = 0 Since the difference is constant, this is an arithmetic sequence. Answer: Arithmetic, d = 0 e) 1.5, 3.0, 4.5, 6.0, ... Step 1: Calculate the differences between consecutive terms. 3.0 - 1.5 = 1.5 4.5 - 3.0 = 1.5 6.0 - 4.5 = 1.5 Since the difference is constant, this is an arithmetic sequence. Answer: Arithmetic, d = 1.5 Send me the next one 📸