Question: How many numbers are in the list $ 2, 5, 8, \ldots, 32 $?
["# How Many Numbers Are in the List $ 2, 5, 8, \ldots, 32 $? A Step-by-Step Guide", "If you've ever come across a sequence like $ 2, 5, 8, \ldots, 32 $, you might be wondering: How many numbers are in this list? This type of question involves understanding arithmetic sequences and applying a simple formula. In this article, we’ll explore how to determine the number of terms in this specific sequence and clarify the math behind it.", "## What Is the List $ 2, 5, 8, \ldots, 32 $?", "The sequence starts at 2 and increases by a common difference of 3.\n- First term ($ a_1 $): 2\n- Common difference ($ d $): 3\n- Last term ($ a_n $): 32", "Such sequences follow the formula for the $ n $-th term:\n[\na_n = a_1 + (n - 1)d\n]", "## Plug in Known Values to Solve for $ n $", "Substitute $ a_1 = 2 $, $ d = 3 $, and $ a_n = 32 $ into the formula:\n[\n32 = 2 + (n - 1) \cdot 3\n]", "Now solve step-by-step:", "1. Subtract 2 from both sides:\n[\n30 = (n - 1) \cdot 3\n]", "2. Divide both sides by 3:\n[\n10 = n - 1\n]", "3. Add 1 to both sides:\n[\nn = 11\n]", "## Conclusion: There Are 11 Numbers in the List", "The list $ 2, 5, 8, \ldots, 32 $ contains exactly 11 numbers. Each term increases uniformly by 3, starting at 2 and ending at 32, following a clear arithmetic pattern.", "## Why This Matters for Math and Test Prep", "Understanding how to count terms in an arithmetic sequence helps build foundational algebra skills. This type of problem appears frequently in school math curricula and standardized tests, training students to recognize patterns and apply formulas efficiently.", "Whether you're a student learning basic sequences or a teacher preparing students for more complex topics, knowing how to calculate the number of terms in an arithmetic list is a valuable skill.", "---", "Keywords: how many numbers in the list 2, 5, 8, ..., 32, arithmetic sequence, number of terms, sequence formula, step-by-step math, educational guide", "Meta Title: How Many Numbers Are in the List $ 2, 5, 8, \ldots, 32 $? | Step-by-Step Explanation\nMeta Description: Discover how to calculate the number of terms in the arithmetic sequence $ 2, 5, 8, \ldots, 32 $ using the common difference and a simple formula.\nHeader Tags: #HowManyNumbersInTheList #ArithmeticSequence #MathTips #AlgebraBasics"]
