A sequence starts with 3, and each term is 4 more than the previous term. What is the sum of the first 12 terms?

Wed, 06 May 2026 11:14:47 +0000

**Why This Simple Sequence Is Conversing More Than You Think**
A sequence starts with 3, and each term increases by 4—3, 7, 11, 15… This pattern, simple in appearance, is gaining quiet attention across the US digital landscape. Beyond numbers, it reflects a growing curiosity about logical sequences, predictable patterns, and accessible mathematical structures—especially among users seeking clarity in complex trends. Whether linked to personal finance forecasting, behavioral algorithmic modeling, or data-driven decision making, understanding incremental progression offers surprisingly broad relevance. The fast-growing interest suggests people are responding to clearer frameworks for analyzing change, growth, and summation. **A Legacy Pattern Appearing in Modern Conversations**
This arithmetic sequence follows a predictable rhythm: starting at 3, each new value adds 4. What makes it notable is how such a basic structure fits naturally into moments of structured thinking. In recent months, discussions around reliable prediction models—used in budgeting, trend forecasting, and even behavioral analytics—have turned this kind of pattern into a relatable metaphor. Mobile-first users scrolling for actionable knowledge now encounter it unexpectedly in content about growth cycles, variable increments, and scalable outcomes. Its symmetry and clarity make it memorable, sparking deeper engagement with mathematical concepts normally buried in formal education. **Breaking Down the Sequence: Step-by-Step**
The sequence begins with 3 and increases by 4 with each step:
Term 1: 3
Term 2: 3 + 4 = 7
Term 3: 7 + 4 = 11
Term 4: 11 + 4 = 15
... and so on. This is an arithmetic sequence where the first term (a) = 3, common difference (d) = 4, and number of terms (n) = 12. The formula for the sum of the first n terms of an arithmetic sequence is:
Sum = n × (2a + (n – 1)d) ÷ 2