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
To find the nth term rule for the pattern 3, 6, 9, 12, 15, , we first need to determine if it's an arithmetic or geometric sequence. Step 1: Find the difference between consecutive terms. 6 - 3 = 3 9 - 6 = 3 12 - 9 = 3 15 - 12 = 3 Since the difference between consecutive terms is constant, this is an arithmetic sequence with a common difference (d) of 3. Step 2: Identify the first term. The first term (a_1) is 3. Step 3: Use the formula for the nth term of an arithmetic sequence. The formula is a_n = a_1 + (n-1)d. Step 4: Substitute the values of a_1 and d into the formula. a_n = 3 + (n-1)3 Step 5: Simplify the expression. a_n = 3 + 3n - 3 a_n = 3n Step 6: Verify the rule with a few terms from the pattern. For n=1, a_1 = 3(1) = 3 For n=2, a_2 = 3(2) = 6 For n=3, a_3 = 3(3) = 9 The rule a_n = 3n correctly generates the terms of the pattern. Comparing this with the given options: A. a_n = n+2 B. a_n = 3n C. a_n = 3n+1 D. a_n = n+3 The correct option is B. The final answer is B. a_n = 3n. Send me the next one 📸