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 identify the pattern and write an algebraic expression for the n-th term of the sequence 2, 5, 8, 11, 14, , we first need to determine if it's an arithmetic or geometric sequence. Step 1: Find the difference between consecutive terms. 5 - 2 = 3 8 - 5 = 3 11 - 8 = 3 14 - 11 = 3 Since the difference between consecutive terms is constant, this is an arithmetic sequence with a common difference d=3. Step 2: Identify the first term. The first term of the sequence, denoted as a_1, is 2. Step 3: Use the formula for the n-th term of an arithmetic sequence. The formula for the n-th term (a_n) of an arithmetic sequence is given by: a_n = a_1 + (n-1)d where a_1 is the first term, n is the term number, and d is the common difference. Step 4: Substitute the values of a_1 and d into the formula. Substitute a_1 = 2 and d = 3: a_n = 2 + (n-1)3 Step 5: Simplify the expression. Distribute the 3: a_n = 2 + 3n - 3 Combine the constant terms: a_n = 3n - 1 The algebraic expression for the n-th term is 3n - 1. What's next?