A sequence is defined by \( a_n = 2n^2 + 3n + 1 \). What is the 10th term of the sequence?
["Understanding Sequences: What is the 10th Term of ( a_n = 2n^2 + 3n + 1 )?", "A sequence is a list of numbers arranged in a specific order, where each term is defined by a formula. One such sequence is defined by the quadratic expression:\n[\na_n = 2n^2 + 3n + 1\n]", "This formula calculates the ( n )-th term of the sequence for any positive integer ( n ). Whether you're studying algebra, mathematics, or exploring patterns in data, understanding how sequences work is essential.", "### How to Find the 10th Term", "To find the 10th term (( a_{10} )), substitute ( n = 10 ) into the formula and perform the calculations step by step:", "[\na_{10} = 2(10)^2 + 3(10) + 1\n]", "First, compute the square:\n[\n10^2 = 100\n]", "Multiply by the coefficient:\n[\n2 \ imes 100 = 200\n]", "Next, calculate the linear term:\n[\n3 \ imes 10 = 30\n]", "Add all parts together:\n[\n200 + 30 + 1 = 231\n]", "### Conclusion", "The 10th term of the sequence defined by ( a_n = 2n^2 + 3n + 1 ) is\n[\n\boxed{231}\n]", "Understanding sequence formulas like this builds a strong foundation for algebra, calculus, and discrete mathematics—key areas for students, educators, and STEM enthusiasts alike."]
