Solution: This is a geometric sequence with $ a = 3 $, $ r = 3 $. The sum of the first $ n $ terms is:

Mon, 04 May 2026 15:09:48 +0000

**Discover Hook: What math concept explains the explosive growth happening across industries right now? A geometric sequence with $ a = 3 $, $ r = 3 $—and its powerful sum formula—is surprisingly relevant in today’s data-driven world.** In a landscape where innovation accelerates rapidly, patterns rooted in mathematics offer unexpected clarity. One such pattern—describing a sequence where each term grows exactly three times the previous—is quietly shaping how experts analyze growth, investment returns, and market trends. This mathematical framework helps decode how values multiply over time, providing insight into exponential change visible in technology adoption, financial forecasting, and demographic shifts. Users exploring efficient models for scaling and forecasting are discovering a foundational principle that influences real-world decision-making. --- **Why This Geometric Sequence Is Gaining Attention in the US**