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
Step 1: Determine the rule for the sequence. We are given the input and output values for the second table: Input (n): 1, 2, 3 Output (T_n): 5, 8, 11 First, find the common difference between consecutive output values: 8 - 5 = 3 11 - 8 = 3 The common difference is 3. This indicates a linear rule of the form T_n = an + b, where a is the common difference. So, a = 3. The rule is T_n = 3n + b. Step 2: Find the value of b. Substitute one of the input-output pairs into the rule. Using n=1 and T_1=5: 5 = 3(1) + b 5 = 3 + b b = 5 - 3 b = 2 The rule for the sequence is T_n = 3n + 2. Step 3: Calculate the missing output values using the rule T_n = 3n + 2. For Input n=4: T_4 = 3(4) + 2 = 12 + 2 = 14 For Input n=10: T_10 = 3(10) + 2 = 30 + 2 = 32 For Input n=100: T_100 = 3(100) + 2 = 300 + 2 = 302 Step 4: Complete the table and list the terms. The rule is: T_n = 3n + 2 The completed table is: Input | 1 | 2 | 3 | 4 | 10 | 100 ---|---|---|---|---|---|--- Output | 5 | 8 | 11 | 14 | 32 | 302 The terms are: T_1 = 5 T_2 = 8 T_3 = 11 T_4 = 14 T_10 = 32 T_100 = 302 Send me the next one 📸