We are given an arithmetic sequence where the first term $ a = 20 $ and the common difference $ d = 8 $. We are to find the total attendance over the first 15 weeks, which means we need to calculate the sum of the first 15 terms of the sequence.
["Discover the Quiet Math Behind Real Growth: Attendance Trends Over 15 Weeks \nPropelled by shifting needs and data-driven planning, increasingly people are turning to structured patterns—like arithmetic sequences—to make sense of weekly engagement and attendance trends. Among the mathematical models gaining quiet traction, one classic example unfolds naturally: a sequence starting at 20 with a steady weekly climb of 8. Used widely in education, staffing, and event forecasting, this pattern reveals how consistent growth shapes real-world outcomes. Calculating the sum of the first 15 terms uncovers a tangible measure of cumulative impact, making it unexpectedly relevant for organizations measuring performance and planning ahead.", "Why This Arithmetic Sequence Matters Now \nAcross the U.S., sectors from education to nonprofit outreach are increasingly applying mathematical models to track participation and engagement. An arithmetic sequence captures the rhythm of gradual weekly progress—whether student attendance rising steadily or a training program hitting consistent attendance milestones. With economic uncertainty and faster lifestyle paces, understanding predictable growth patterns supports better decision-making. People are naturally drawn to clear trends, and this sequence offers a reliable, transparent way to quantify what might otherwise feel vague or unpredictable.", "Understanding the Basics: What We’re Working With \nWe begin with an arithmetic sequence defined by first term $ a = 20 $ and common difference $ d = 8 $. This means each week adds 8 more participants than the prior—20 the first, 28 the second, 36 the third, and so on. The formula for the sum of the first $ n $ terms, $ S_n $, is $ S_n = \frac{n}{2}(2a + (n-1)d) $. For $ n = 15 $, this reveals the total attendance not as a random number, but as a structured outcome of incremental steps—natural in any progression with consistent growth.", "Step-by-Step: Calculating the First 15 Weeks’ Sum \nStart with the formula: \n$ S_{15} = \frac{15}{2} \left(2 \ imes"]
