Substitute \(n = 10\) into the formula: \(a_{10} = 2 \times 10 + 3\).
["# Understanding the Formula: (a_{10} = 2 \ imes 10 + 3)", "If you're exploring sequences generated by simple mathematical formulas, one common assignment involves finding a specific term using a defined rule. A straightforward example is the recurring formula:", "[\na_n = 2 \ imes n + 3\n]", "When applied with (n = 10), this becomes:", "[\na_{10} = 2 \ imes 10 + 3\n]", "This simple expression offers a useful opportunity to understand how arithmetic sequences are evaluated using direct substitution, making it an essential concept in algebra, sequences, and elementary mathematics.", "## What Does (a_{10} = 2 \ imes 10 + 3) Mean?", "In this formula:\n- (a_n) represents the (n)-th term in a sequence.\n- (n = 10) means we want the term located at the tenth position.\n- The expression (2 \ imes 10 + 3) calculates the value of the 10th term using the given rule.", "This formula follows a linear pattern: each term increases by a fixed amount (defined by the coefficients and constant). Here, the term grows by 2 for each increment in (n), starting from an initial offset.", "## Calculating (a_{10}): Step-by-Step", "To find (a_{10}), substitute (n = 10) directly into the formula:", "[\na_{10} = 2 \ imes 10 + 3\n]", "First, multiply:", "[\n2 \ imes 10 = 20\n]", "Then, add the constant:", "[\n20 + 3 = 23\n]", "Thus, the value of the 10th term is:", "[\na_{10} = 23\n]", "## Why Is This Formula Useful?", "While simple, the formula (a_n = 2 \ imes n + 3) illustrates core principles in sequences such as linearity and predictability. It helps students and learners recognize how algebraic expressions model real-world linear growth—from defining budgets and trends to solving everyday problems involving patterns.", "Moreover, practicing direct substitution like this strengthens foundational algebra skills, preparing learners for more complex sequences involving exponents, recursion, or nonlinear relationships.", "## Summary", "Using the formula (a_{10} = 2 \ imes 10 + 3):\n- Direct substitution yields (a_{10} = 23).\n- The term grows linearly by adding 2 repeatedly.\n- This example reinforces basic but vital algebraic operations.", "Whether studying sequences in school or building foundational math skills, mastering direct substitutions empowers better understanding and problem-solving.", "---", "Key Takeaway: Substituting (n = 10) into (a_n = 2n + 3) is a clear and valuable exercise in evaluating arithmetic sequences, demonstrating how simple linear formulas produce specific term values through straightforward calculation."]
