A geometric sequence has a first term of 3 and a common ratio of 2. What is the sum of the first 7 terms?

Sat, 18 Apr 2026 06:33:46 +0000

**A geometric sequence starts with 3 and has a common ratio of 2—here’s how the sum of the first 7 terms unfolds** What if you began with just 3 and doubled it seven times—would you expect a manageable number, or a rapid climb? This simple math pattern reveals more than just numbers; it’s a common model used across science, finance, and digital trends. A geometric sequence with a first term of 3 and a common ratio of 2 means each term doubles the previous—3, 6, 12, 24, and so on. Curious about what happens when you sum the first seven of these? The result isn’t just a number—it’s a glimpse into a powerful mathematical concept shaping real-world decisions. Understanding how geometric sequences grow helps explain patterns in interest accumulation, viral content spread, and algorithmic recommendations. In the US, where data literacy and smart financial planning are on the rise, this sequence models straightforward exponential growth seen in investments, population trends, and even social engagement online. The sum of the first seven terms reveals how quickly small starting points can build substantial impact over time. **Why the geometric sequence with first term 3 and ratio 2 is trending in US digital culture**