A geometric sequence starts with the term 5 and has a common ratio of 3. What is the 6th term of the sequence?

Sat, 02 May 2026 18:34:44 +0000

**Unlocking Patterns: The Quiet Power of Geometric Sequences**
Why are more students and professionals pausing to unpack the rhythm of numbers that multiply—starting with 5 and growing by three each step? The sequence begins 5, 15, 45, and follows a clear rule: multiply by 3 each time. This process, called a geometric sequence, reveals how patterns shape data trends, algorithms, and financial growth models across industries. With rising interest in structured logic and predictive systems, understanding such sequences offers insight into structured thinking with real-world impact. On mobile-connected platforms, curiosity about mathematical sequences is seeing new engagement—users exploring how predictable patterns inform decision-making, from investment strategies to data science. This simple yet powerful sequence illustrates how exponential growth unfolds quietly behind complex phenomena. **The Spread of the Sequence: From Term 1 to Term 6**
Starting with 5 and multiplying by 3 each step, the next terms unfold naturally:
Term 1: 5
Term 2: 5 × 3 = 15
Term 3: 15 × 3 = 45
Term 4: 45 × 3 = 135
Term 5: 135 × 3 = 405
Term 6: 405 × 3 = 1,215 This progression demonstrates exponential acceleration—each term builds directly on the previous through steady multiplication. For US learners and professionals navigating data trends, predictable sequences like this offer a foundation for interpreting growth patterns in everything from technology to finance. Dive deeper into how these patterns shape real-world models on mobile devices. **Cultural and Digital Trends Fueling Interest**
The fascination with geometric sequences reflects broader trends in computational thinking and digital literacy. In classrooms and online resources, educators emphasize structured patterns to build critical reasoning. On mobile platforms, short, clarifying content on math and logic now receives stronger engagement from learners seeking clear, factual explanations. With rising curiosity about data patterns, sequences such as 5, 15, 45, 135, 405, 1,215 serve as accessible entry points into exponential growth—shaping how users understand change, forecasting, and scalable systems. This has solidified geometric sequences as more than classroom exercises—they’re part of the language of modern data literacy.