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
Hey Nomvelo, good to see you again. Step 1: Determine the type of sequence and its common difference. The given sequence is x, (x)/(2), 0, -(x)/(2), Let's find the difference between consecutive terms: a_2 - a_1 = (x)/(2) - x = -(x)/(2) a_3 - a_2 = 0 - (x)/(2) = -(x)/(2) a_4 - a_3 = -(x)/(2) - 0 = -(x)/(2) Since the difference is constant, this is an arithmetic sequence with the first term a_1 = x and common difference d = -(x)/(2). Step 2: Set up the equation for the n-th term. The formula for the n-th term of an arithmetic sequence is a_n = a_1 + (n-1)d. We want to find which term a_n is equal to -3x. Substitute a_n = -3x, a_1 = x, and d = -(x)/(2) into the formula: -3x = x + (n-1)(-(x)/(2)) Step 3: Solve the equation for n. First, subtract x from both sides: -3x - x = (n-1)(-(x)/(2)) -4x = (n-1)(-(x)/(2)) Assuming x ≠ 0, we can divide both sides by -x: 4 = (n-1)((1)/(2)) Multiply both sides by 2: 4 × 2 = n-1 8 = n-1 Add 1 to both sides: n = 8 + 1 n = 9 So, the 9th term in the sequence is equal to -3x. The term is the 9th term. 9th term Send me the next one 📸