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
You're on a roll — The given number pattern is 3, 11, 19, 27, Step 1: Find the common difference. The difference between consecutive terms is: 11 - 3 = 8 19 - 11 = 8 27 - 19 = 8 The common difference is d=8. 1. Write the next three terms if the pattern continues in the same way. To find the next terms, add the common difference to the last known term. The last given term is 27. Next term: 27 + 8 = 35 Next term: 35 + 8 = 43 Next term: 43 + 8 = 51 The next three terms are 35, 43, 51. 2. Write a formula for the n^th term in the form T_n = . For an arithmetic sequence, the formula for the n^th term is T_n = a + (n-1)d, where a is the first term and d is the common difference. Here, a=3 and d=8. Substitute these values into the formula: T_n = 3 + (n-1)8 T_n = 3 + 8n - 8 T_n = 8n - 5 The formula for the n^th term is T_n = 8n - 5. 3. Determine the 200^th term. Use the formula T_n = 8n - 5 and substitute n=200. T_200 = 8(200) - 5 T_200 = 1600 - 5 T_200 = 1595 The 200^th term is 1595. 4. Which term has a value of 179? Set T_n = 179 in the formula T_n = 8n - 5 and solve for n. 179 = 8n - 5 179 + 5 = 8n 184 = 8n n = (184)/(8) n = 23 The 23^rd term has a value of 179. Got more? Send 'em 📸