A geometric sequence has a first term of 5 and a common ratio of 3. What is the 4th term?
["A geometric sequence has a first term of 5 and a common ratio of 3. What is the 4th term?", "Curious about patterns in numbers? A geometric sequence offers a clear, logical way to explore growth—one term at a time. When the first term is 5 and the common ratio is 3, each successive number multiplies by 3. This simple yet powerful concept is quietly shaping fields from finance to digital scaling, sparking interest in how sequences inform data, design, and decision-making.", "The sequence begins: 5 (first term), then \n5 × 3 = 15 (second term), \n15 × 3 = 45 (third term), \n45 × 3 = 135 (fourth term).", "That makes the fourth term 135. While this might seem straightforward, the real value lies in understanding how geometric progressions model exponential growth—how small shifts can lead to significant outcomes over time.", "### Why a geometric sequence with first term 5 and ratio 3 is gaining attention in the US", "In a digital landscape where exponential growth is both familiar and vital—think fintech, app user acquisition, or viral content trends—this mathematical structure offers a clean framework for modeling change. The consistent multiplication of 3 reflects reliability and rapid progression, qualities quality professionals and data analysts seek.", "Beyond pure math, such sequences are increasingly highlighted in educational platforms, personal finance apps, and even startup strategy guides. They illustrate core principles of compounding, scalability, and forecasting—concepts critical to innovation and growth in today’s economy.", "### How a geometric sequence works: The math behind the 4th term", "In a geometric sequence, every term is generated by multiplying the previous one by a fixed value—the common ratio. With a first term of 5 and a ratio of 3, the formula for any term \(n\) is:", "\[ a_n = a_1 \ imes r^{(n-1)} \] \nWhere: \n- \(a_1 = 5\) (first term) \n- \(r = 3\) (common ratio) \n- \(n = 4\) (the term we want)", "Plugging in: \n\[ a_4 = 5 \ imes 3^{(4-1)} = 5 \ imes 3^3 = 5 \ imes 27 = 135"]
