A geometric sequence has a first term of 3 and a common ratio of 4. What is the sum of the first 5 terms?

Wed, 29 Apr 2026 19:22:04 +0000

A geometric sequence is a pattern of numbers where each term after the first is found by multiplying the previous one by a fixed value—the common ratio. When a sequence starts with 3 and multiplies each term by 4, the first five terms follow a clear mathematical progression that captures interest across educational platforms and real-life problem-solving contexts. Understanding how to calculate this sum isn’t just academic—it aligns with rising curiosity in personal finance, data literacy, and STEM exploration, especially among US audiences using mobile devices to seek informative content. The first five terms of this sequence are 3, 12, 48, 192, and 768. Adding them together yields a total of 1,023. This progression illustrates exponential growth—a concept central to trends in investing, technology adoption, and long-term planning. Because every term grows rapidly due to consistent multiplication, the sum reflects compounding effects, which resonate with users exploring savings strategies, population modeling, or complex financial forecasts. In recent years, increasing attention on geometric sequences has emerged in digital learning environments, driven by a broader push to strengthen math literacy and critical thinking skills. People are drawn to such topics not only for academic value but for practical insights into how small, consistent changes can lead to significant outcomes over time—relevant in budgeting, retirement planning, and even app growth analytics. While explicit sexual content or clickbait tactics have no place here, this subject nurtures curiosity through clear, neutral explanations that empower informed decision-making. Common questions often center on how to compute such sums accurately and why exponential progression matters beyond the classroom. For example:
- H3: *Why Is Exponential Growth Important?*
Exponential sequences model real-world phenomena like compound interest, virus spread, and digital engagement—making understanding them key for informed participation in modern economic and social systems.
- H3: *How to Calculate the Sum Without Confusion*
Start with the first term and common ratio, then apply the formula for the sum of a finite geometric series:
\[ S_n = a