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
Here are the solutions to the problems: 5.1 Step 1: Calculate the difference between consecutive terms. The terms are 5, 9, 13, 17, 21. 9 - 5 = 4 13 - 9 = 4 17 - 13 = 4 21 - 17 = 4 The difference between the consecutive terms is 4. 5.2 Step 1: Complete the expressions using the first term (5) and the common difference (4). The general form for an arithmetic sequence is T_n = a + (n-1)d, where a is the first term and d is the common difference. Here, a=5 and d=4. The 1st term = 5 The 2nd term = 5 + (2-1) × 4 = 5 + 1 × 4 The 3rd term = 5 + (3-1) × 4 = 5 + 2 × 4 The 4th term = 5 + (4-1) × 4 = 5 + 3 × 4 The 5th term = 5 + (5-1) × 4 = 5 + 4 × 4 The 6th term = 5 + (6-1) × 4 = 5 + 5 × 4 The completed expressions are: The 1st term = 5 The 2nd term = 5 + 1 × 4 The 3rd term = 5 + 2 × 4 The 4th term = 5 + 3 × 4 The 5th term = 5 + 4 × 4 The 6th term = 5 + 5 × 4 5.3 Step 1: Describe the rule for finding a term in any position. The rule for finding a term in any position in this sequence is to start with the first term (5), then add the product of the common difference (4) and one less than the term's position. This can be written as T_n = 5 + (n-1) × 4, where T_n is the term at position n. Send me the next one 📸