A geometric sequence has a first term of 3 and a common ratio of 2. What is the sum of the first 10 terms?

Mon, 04 May 2026 05:47:44 +0000

**What Is a Geometric Sequence? How Knowing Its Sum Matters in the US Digital Landscape** Ever come across a math pattern that feels like a financial forecast or trends in tech growth—something built on a steady, doubling foundation? Enter the geometric sequence: a foundational concept where each term grows by a consistent ratio. For example, starting with 3 and multiplying by 2 each time, the sequence unfolds as 3, 6, 12, 24, and so on. Now, the big question: What’s the sum of the first 10 terms? Beyond the equation, understanding this concept reveals hidden logic behind exponential trends—used in finance, technology adoption, and data growth modeling across the US market. A geometric sequence is defined by its first term and common ratio. The formula for summing the first *n* terms—*Sₙ = a(1 - rⁿ)/(1 - r)* when *r ≠ 1*—lets us calculate this total efficiently. With *a = 3* and *r = 2*, plugging in gives *S₁₀ = 3(1 - 2¹⁰)/(1 - 2)*. Simplifying, this reveals the sum equals 3(1 - 1024)/(-1) = 3 × 1023 = 3069. This isn’t just a number—it’s a gateway to understanding exponential accumulation. Interest in this type of math is rising in the US, fueled by online education, STEM engagement, and curiosity about how data patterns shape digital behavior. People exploring investing, app growth, or AI adoption often encounter sequences like this behind the scenes. Recognizing geometric progression offers clarity, helping users decode exponential growth in real-world scenarios.