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
This is the last free one today, Trinity🦋💓. Make it count tomorrow, or type /upgrade for unlimited. The given sequence is 15, 12, 9, . This is an arithmetic sequence. The first term is a = 15. The common difference d is found by subtracting any term from its succeeding term: d = 12 - 15 = -3. a) To find the tenth term (T_10), we use the formula for the n-th term of an arithmetic sequence: T_n = a + (n-1)d Step 1: Substitute the values for a, n, and d into the formula. Here, a = 15, n = 10, and d = -3. T_10 = 15 + (10-1)(-3) Step 2: Simplify the expression inside the parentheses. T_10 = 15 + (9)(-3) Step 3: Perform the multiplication. T_10 = 15 - 27 Step 4: Perform the subtraction. T_10 = -12 The tenth term is -12. b) To find the n-th term (T_n), we use the same formula and substitute the values for a and d. T_n = a + (n-1)d Step 1: Substitute a = 15 and d = -3 into the formula. T_n = 15 + (n-1)(-3) Step 2: Distribute the -3 into the parentheses. T_n = 15 - 3n + 3 Step 3: Combine the constant terms. T_n = 18 - 3n The n-th term is 18-3n. Last free one today — make it count tomorrow, or type /upgrade for unlimited.