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

Fri, 17 Apr 2026 04:37:52 +0000

**Unlocking Patterns: How a Geometric Sequence Shapes Math Learning and Real-World Decisions** Ever wonder how simple numbers can reveal hidden order in the world around you? Right now, more learners, educators, and professionals are exploring structured number patterns—not just as abstract concepts, but as tools to think critically about trends, investments, and growth. One classic example drawing growing attention is the geometric sequence: a pattern where each term grows by a fixed ratio. Take the sequence starting with 5 and a common ratio of 3—where each number multiplies by 3 to get the next. The first four terms unfold as 5, 15, 45, and 135. Adding them together reveals a sum of 200—yet this simple calculation opens doors to deeper understanding. Why is this sequence so relevant, and how does mastering such patterns empower everyday decision-making? --- ### Why This Geometric Pattern Is Resonating Now