Premier terme 15, dernier 90, raison 15. Résolvez \(15 + (n-1) \times 15 = 90 \Rightarrow n = 6\).

["Understanding the Premier Terme 15, Dernier 90, Raison 15: Solving (15 + (n-1) \ imes 15 = 90)", "Ever come across the equation (15 + (n-1) \ imes 15 = 90) and wonder what it means? This expression is more than just math—it reveals a logical pattern often used in scenarios involving sequences, progressions, or structured progressions like the “Premier Terme 15, Dernier 90, Raison 15.” Let’s break it down and explore its solution: (n = 6), and why this matters.", "### What is Premier Terme, Dernier Terme, and Raison?", "- Premier Terme (First term): This is the starting value in an arithmetic sequence.\n- Dernier Terme (Last term): The final value in the sequence.\n- Raison (Common difference): The constant amount added to get from one term to the next.", "In many educational or algorithmic contexts—such as word problems or learning sequences—this formula models scenarios like climbing steps, incremental progress, or repeated intervals.", "### Step-by-Step Solution: Solving (15 + (n-1) \ imes 15 = 90)", "This equation expresses an arithmetic progression starting at 15, increasing by 15 each step (the “raison”), and seeking how many total terms (n) reach exactly 90.", "We solve:\n[\n15 + (n-1) \ imes 15 = 90\n]", "Step 1: Subtract 15 from both sides:\n[\n(n-1) \ imes 15 = 75\n]", "Step 2: Divide both sides by 15:\n[\nn-1 = 5\n]", "Step 3: Add 1:\n[\nn = 6\n]", "This reveals there are 6 terms in the sequence starting at 15, increasing by 15 each time, where the sixth term is exactly 90.", "### Sequence Breakdown", "Following the progression:\n- 1st term: 15\n- 2nd term: 15 + 15 = 30\n- 3rd term: 30 + 15 = 45\n- 4th term: 45 + 15 = 60\n- 5th term: 60 + 15 = 75\n- 6th term: 75 + 15 = 90", "### Real-World Application: Why This Format?", "This mathematical structure appears in teaching progression-based thinking—like saving $15 weekly onward, each term representing total savings, or digital systems advancing in discrete intervals. The equation balances constant steps ((15 \ imes (n-1))) with an initial jump (Premier Terme = 15), efficiently modeling growth from a fixed base.", "---", "Conclusion:\nThe equation (15 + (n-1) \ imes 15 = 90) elegantly solves to (n = 6), illustrating a simple yet powerful arithmetic progression. Understanding such sequences builds stronger problem-solving skills in math, logic puzzles, and algorithmic thinking—key foundations in education and real-world applications. Whether you’re calculating savings, steps in a staircase, or algorithmic iterations, recognizing the pattern of Premier Terme, raison, and Dernier Terme turns abstract problems into clear, solvable paths."]