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
Your workings are correct! Here's a breakdown of the steps shown in the image, which align with the standard methods for arithmetic sequences: 1. Identify the first term (a) and common difference (d): The sequence is 6, 10, 14, 18, First term, a = 6. Common difference, d = 10 - 6 = 4. 2. Find the n-th term (U_n or a_n): The formula for the n-th term of an arithmetic sequence is U_n = a + (n-1)d. Substituting the values: U_n = 6 + (n-1)4 U_n = 6 + 4n - 4 U_n = 4n + 2 This is correct. 3. Find the sum of the first n terms (S_n): The formula for the sum of the first n terms of an arithmetic sequence is S_n = (n)/(2)(2a + (n-1)d). Substituting the values: S_n = (n)/(2)(2(6) + (n-1)4) S_n = (n)/(2)(12 + 4n - 4) S_n = (n)/(2)(4n + 8) S_n = n(2n + 4) S_n = 2n^2 + 4n This is also correct. Your solution matches the correct derivation for both the n-th term and the sum of the first n terms of the given arithmetic sequence.