A geometric sequence has first term 3 and common ratio 2. Find the 8th term.
["A geometric sequence has first term 3 and common ratio 2. Find the 8th term. \nPeople frequently explore geometric patterns in finance, computer science, and design, making sequences like this increasingly relevant beyond the classroom. When someone asks, “What’s the 8th term of a geometric sequence starting at 3 with a ratio of 2?” they’re often uncovering hidden structures in data growth, investment compounding, or digital scaling—all key topics shaping modern decision-making.", "With a first term of 3 and a constant ratio of 2, each term doubles the last. Starting at 3, the sequence builds as 3, 6, 12, 24, and so on. At this pace, the pattern follows a clear formula: \( a_n = a_1 \ imes r^{(n-1)} \). This simple yet powerful structure underpins rapid progression—whether in algorithmic development or exponential user growth—dominating discussions across tech, education, and investment communities.", "Using the formula, the 8th term calculates simply: \( a_8 = 3 \ imes 2^{(8-1)} = 3 \ imes 128 = 384 \). Thirds, sixths, and beyond represent foundational steps in mastering exponential relationships—skills increasingly valuable in data literacy and financial planning.", "Why This Sequence Is Gaining Attention \nAcross the United States, interest in geometric sequences—especially those with small, consistent ratios—is rising in education platforms and finance literacy initiatives. As personal finance apps and online learning tools emphasize pattern recognition, the predictable growth of sequences like this helps users understand compound trends in savings, investments, and data usage. The simplicity of the 3-starting ratio with doubling growth makes it an accessible gateway to more complex mathematical and analytical thinking.", "Moreover, digital systems—from streaming recommendation engines to scaling social networks—rely on geometric progressions. This real-world relevance fuels curiosity, driving users to uncover these principles behind visible changes in speed"]
