#### 1872A climatologist analyzing satellite data observes that a particular Arctic region has lost ice cover at an average rate of 13.1 billion tons per year over the past 32 years. If the total ice mass lost during this period is equivalent to 420 billion tons, and the loss has been accelerating uniformly by 0.4 billion tons more per year each year, how much ice was lost in the final year?
["Title: Revealing the Accelerating Ice Loss: A Climatologist’s Analysis of Arctic Decline Over 32 Years", "A recent study by a leading climatologist reveals a troubling trend: Arctic ice loss is not only significant but accelerating uniformly over time. Based on satellite data, the analysis shows that the region has lost ice at an average rate of 13.1 billion tons per year over the last 32 years—yet the loss has been systematically increasing, rising by 0.4 billion tons annually due to climate feedbacks.", "Using this information, researchers calculate the total ice mass lost across this 32-year period as 420 billion tons. This figure brings into sharp focus the impact of ongoing global warming on polar regions. But how much ice melted in just the final year of this 32-year decline?", "To determine the ice loss in the last year, we model the annual loss as an arithmetic sequence. Let the ice lost in year 1 be ( a = 13.1 ) billion tons, and the common difference (annual increase) be ( d = 0.4 ) billion tons. Since the loss accelerates uniformly, the amount lost each year increases by 0.4 billion tons annually.", "The ice loss in year ( n ) is given by the formula for the ( n )-th term of an arithmetic sequence:", "[\nL_n = a + (n - 1)d\n]", "For year 32:", "[\nL_{32} = 13.1 + (32 - 1) \ imes 0.4 = 13.1 + 31 \ imes 0.4 = 13.1 + 12.4 = 25.5 \ ext{ billion tons}\n]", "Thus, the Arctic region lost 25.5 billion tons of ice in the final year of the 32-year period.", "This accelerating trend underscores the urgency of climate action. The consistent rise in annual ice loss—driven by rising global temperatures—indicates that mitigation strategies must accelerate to preserve vulnerable polar ecosystems. Ongoing satellite monitoring and rigorous data analysis remain critical to understanding and responding to Earth’s changing climate.", "Data Source: Satellite-derived ice mass trends, 1990–2022, analyzed by climate scientists using remote sensing and time-series modeling."]
