A sequence is defined by \(a_n = 3n^2 + 2n + 1\). Find the 5th term of the sequence.

["Understanding Sequences: How to Find the 5th Term of ( a_n = 3n^2 + 2n + 1 )", "A sequence is a list of numbers arranged in a predictable pattern based on the position of each term, typically defined by a rule or formula. In this article, we explore how to calculate a specific term in a quadratic sequence defined by the formula:", "[\na_n = 3n^2 + 2n + 1\n]", "Our focus is on finding the 5th term, ( a_5 ), using this formula.", "---", "### What is the 5th Term in a Sequence?", "The 5th term means we substitute ( n = 5 ) into the formula for ( a_n ). This involves evaluating the polynomial expression at ( n = 5 ).", "---", "### Step-by-Step Calculation of ( a_5 )", "We start with the given formula:", "[\na_n = 3n^2 + 2n + 1\n]", "Substitute ( n = 5 ):", "[\na_5 = 3(5)^2 + 2(5) + 1\n]", "Now compute each part:", "- ( 5^2 = 25 )\n- ( 3 \ imes 25 = 75 )\n- ( 2 \ imes 5 = 10 )", "Putting it all together:", "[\na_5 = 75 + 10 + 1 = 86\n]", "---", "### Conclusion", "The 5th term of the sequence defined by ( a_n = 3n^2 + 2n + 1 ) is:", "[\n\boxed{86}\n]", "Understanding how to evaluate terms in a sequence using algebraic formulas helps in solving a wide range of problems in mathematics, from simple arithmetic progressions to complex polynomial sequences. Whether you're studying for school or exploring self-study, mastering such techniques is essential for success in algebra and beyond.", "---", "Keywords:\nsequence definition, ( a_n ) formula, arithmetic sequence, quadratic sequence, find ( a_5 ), algebraic evaluation, polynomial terms, mathematical formulas, step-by-step math."]