A geometric sequence starts with 5, and each term is multiplied by 3. What is the 6th term?

Mon, 04 May 2026 22:01:49 +0000

**A geometric sequence starts with 5, and each term is multiplied by 3. What is the 6th term?** Have you ever paused while thinking about patterns in numbers? One fascinating sequence that quietly fascinates math learners is the geometric progression—where each term multiplies a fixed number from the one before it. The moment you see this pattern starts with 5 and grows by a factor of 3, it becomes a natural curiosity: if the first term is 5 and every next term is 3 times the previous, how far does this sequence go? The 6th term isn’t just a number—it’s part of a predictable, elegant rule used across math, finance, and data trends. Solving for it builds foundational number sense in a simple, satisfying way. This sequence follows a clear mathematical rule: multiply each term by 3 to get the next version. Starting at 5, the terms unfold steadily: 5, 15, 45, 135, 405, then comes the 6th term. When you multiply 405 by 3, the result is 1,215. So the 6th term is 1,215—a strong demonstration of exponential growth in action. Why is this pattern gaining attention in the US today? Geometric sequences model real-world growth—whether in savings with compound interest, population expansion, or digital content engagement. They serve as a foundational concept in STEM education and financial literacy, helping people understand how small beginnings compound over time. The repetitive multiplication by a consistent ratio makes this sequence intuitive for learners seeking clarity in complex trends.