A geometric sequence has a first term of 2 and a common ratio of 3. What is the sum of the first 6 terms?

Fri, 17 Apr 2026 06:54:21 +0000

**Why Curiosity Around Numbers Is More Common Than Expected**
In a digital world flooded with quick answers, a simple math concept often resurfaces in user searches: the sum of a geometric sequence. Right now, curiosity about structured patterns like 2, 6, 18, 54—followed by 162 as the sixth term—sparks quiet interest. People aren’t browsing for odds or fate; they’re seeking clear, accurate calculations behind repeating patterns. Understanding how these sequences build offers more than just a numerical stretch—it gives insight into logic, prediction, and order in data-driven decisions. This pattern, starting with 2 and growing by multiplying by 3 each time, reveals how exponential growth unfolds across a small number of terms. Users are drawn to it because it’s a foundational concept with tangible applications in finance, design, and science. **Why This Sequence Is Influencing Talk Right Now**
The rise of visually oriented content in platforms like Discover reflects shifting user focus toward digestible depth. Users don’t just want a number—they want to see how it’s derived. With educational trends emphasizing process over product, sequences like this offer rich examples of exponential progression—widely used in compound interest models, population studies, and digital scaling algorithms. At the same time, curiosity about math roots grows amid a broader cultural interest in data literacy. This sequence isn’t flashy, but its clarity and predictability resonate across demographics, especially among users exploring trends through logical frameworks instead of trends-for-trends’ sake. **How the Sum Unfolds: A Clear, Step-by-Step Insight**
The sum of the first six terms in a geometric sequence follows a known formula: Sₙ = a(1 – rⁿ)/(1 – r), where *a* is the first term, *r* the common ratio, and *n* the number of terms. Here, *a* = 2, *r* = 3, and *n* = 6.
Plugging in: S₆ = 2(1 – 3⁶)/(1 – 3) = 2(1 – 729)/(–2) = 2(–728)/(–2) = 728.
The first six terms are: 2, 6, 18, 54, 162, 486. Adding them: 2 + 6 + 18 + 54 + 162 + 486 = 728. This steady increase from way small to rapid growth illustrates how multiplying by 3 repeatedly expands a base value into significant scale—ideal for modeling fast-rising trends or capstone values. **Common Questions People Ask**
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