A sequence is defined by \( a_n = 2n^2 + 3n + 1 \). What is the 10th term?

["Title: Find the 10th Term of the Sequence Defined by ( a_n = 2n^2 + 3n + 1 )", "A sequence is an ordered list of numbers where each term follows a specific rule. In this case, the sequence is defined by the formula:", "[\na_n = 2n^2 + 3n + 1\n]", "Understanding the ( n )-th term of a sequence helps in predicting values without listing all previous terms. In this article, we’ll determine the 10th term using the given formula and explain how to compute any term efficiently.", "### How to Find the 10th Term", "To find the 10th term, substitute ( n = 10 ) into the expression:", "[\na_{10} = 2(10)^2 + 3(10) + 1\n]", "Now calculate each part step-by-step:", "- ( 10^2 = 100 )\n- ( 2 \ imes 100 = 200 )\n- ( 3 \ imes 10 = 30 )\n- The constant term is ( 1 )", "Add them together:", "[\na_{10} = 200 + 30 + 1 = 231\n]", "### Final Answer", "The 10th term of the sequence is:", "[\n\boxed{231}\n]", "---", "Why This Formula Matters\nUsing ( a_n = 2n^2 + 3n + 1 ) allows fast computation for any term, making pattern recognition and mathematical analysis efficient. Whether for academic purposes, coding, or real-world modeling, knowing the rule and how to apply it is essential to master sequences.", "Feel free to use this formula to find any term — just plug in the value of ( n ), apply the operations, and simplify!"]