The sum of the first n terms of an arithmetic sequence is 153, with first term 5 and common difference 3. Find n. - Sourci
How to Solve for n When the Sum of an Arithmetic Sequence Is 153
How to Solve for n When the Sum of an Arithmetic Sequence Is 153
Ever stumbled across a math puzzle that stirred quiet fascination? The sum of the first n terms of an arithmetic sequence hitting 153—starting at 5 with a common difference of 3—might seem like a quiet equation, yet it’s quietly resonating in digital spaces. Curious minds are naturally drawn to puzzles that connect logic, curiosity, and real-world patterns. This article breaks down how to decode the value of n behind this sum—without sensationalism, preserving clarity, accuracy, and relevance to today’s US audience.
The sum of the first n terms of an arithmetic sequence is 153, with first term 5 and common difference 3. Find n.
Understanding the Context
Why This Calculation Is Gaining Attention
In recent years, linear learning—particularly through educational apps and social platforms—has sparked curiosity in how simple math models real-life scenarios. The arithmetic sequence offers a clean, predictable pattern: start at 5, rise by 3 each step. The idea that such a structure fits a total of 153 invites deeper exploration. Users searching online aren’t news-seekers—they’re learners, students, educators, and professionals using math to understand trends, budgets, or growth models. This problem reflects a broader trend: people seeking clarity in numbers behind everyday experiences. Platforms that deliver clear, factual explanations earn trust and visibility, especially on mobile where curious users scroll quickly but linger on trusted insights.
How It Actually Works: A Clear Explanation
An arithmetic sequence follows a fixed pattern: each term increases by a constant difference—in this case, 3. The general formula for the sum of the first n terms is:
Image Gallery
Key Insights
Sₙ = n/2 × (2a + (n−1)d)
Where:
Sₙ = sum of the first n terms
a = first term = 5
d = common difference = 3
n = number of terms (what we’re solving for)
Plugging in known values:
153 = n/2 × (2×5 + (n−1)×3)
153 = n/2 × (10 + 3n − 3)
153 = n/2 × (3n + 7)
Multiply both sides by 2:
🔗 Related Articles You Might Like:
📰 pomeranian dog price 📰 pomme puree 📰 pommes puree 📰 You Wont Believe How Capital Rxs Method Enhances Every Treatmentwhat They Wont Tell You 981819 📰 Youll Never Let Them Gothe Hilarious Chaos Of Adopting Puppies Compiled 1137043 📰 Culligan Drink Wtr Filter Us 600 3823036 📰 Fortnite Replay 📰 S8 Themes Download 1749393 📰 Safetynet Test 📰 Charli Xcx Song About Taylor Swift 📰 The Scoth Snyder Phenomenon The Dark Missteps That Changed Every Epic He Writes 197320 📰 Verizon Wireless West Haverstraw 📰 Financing Vehicle Calculator 2729980 📰 You Wont Believe These 10 Hidden Treasures Unveiled At World Book Day 974980 📰 This Board Drawing Board Auto Unlocks Creativity You Never Knew You Had 5762819 📰 Nick Caley 740780 📰 Roblox Character Finder 📰 Verizon Mac BookFinal Thoughts
306 = n(3n + 7)
306 = 3n² + 7n
Rearranging into standard quadratic form:
3n² + 7n — 306 = 0
Apply the quadratic formula: n = [-b ± √(b² − 4ac)] / 2a
With a = 3, b = 7, c = -306:
Discriminant: b² − 4ac = 49 + 3672 = 3721
√3721 = 61
n = [-7 ± 61] / 6
Two solutions:
n = (−7 + 61)/6 = 54/6 = 9
n = (−7 − 61)/6 = −68/6 (discard—n must be positive)
Therefore, n = 9 is the solution.
Verification: Sum of first 9 terms with a = 5, d = 3:
S₉ = 9/2 × (2×5 + 8×3) = 4.5 × (10 + 24) = 4.5 × 34 = 153 — confirms accuracy.
