The sum of an arithmetic series is 210, with the first term as 3 and the last term as 45. How many terms are in the series?
["The sum of an arithmetic series is 210, with the first term as 3 and the last term as 45. How many terms are in the series? \nThis simple yet intriguing math problem is sparking quiet interest across math communities, study groups, and study-focused mobile users in the U.S. Many ask: how do we find the number of terms when the beginning, end, and total sum are known? It’s a classic puzzle at the intersection of algebra and practical application—something students, educators, and self-learners regularly explore.", "## Why This Problem Is Part of a Broader Conversation \nIn a time when curiosity-driven learning thrives on mobile devices and curated discovery, questions like “how many terms in the series sum to 210, starting at 3 and ending at 45?” reflect a growing interest in logic-based problem solving. This particular series draws attention not just for its numbers, but because it models real-world scenarios—like income planning, resource allocation, or data pattern analysis—making it relevant beyond textbooks. As more Americans seek accessible ways to build analytical thinking, problems involving arithmetic series are gaining traction, especially amid increased focus on STEM and foundational quantitative literacy.", "## How the Sum of an Arithmetic Series Works—is This Application Straightforward? \nThe sum of an arithmetic series is calculated using the formula: \n\[ S = \frac{n}{2} \ imes (a_1 + a_n) \] \nwhere \( S \) is the total sum, \( n \) the number of terms, \( a_1 \) the first term, and \( a_n \) the last term. For this series, \( S = 210 \), \( a_1 = 3 \), and \( a_n = 45 \). Plugging in: \n\[ 210 = \frac{n}{2} \ imes (3 + 45) = \frac{n}{2} \ imes 48 \] \nSimplifying gives: \n\[ 210 = 24"]
