l = a + (n-1)d \implies 996 = 108 + (n-1) \cdot 12 - AIKO, infinite ways to autonomy.
Understanding the Formula: How to Solve for n Using L = a + (n – 1)d
With Step-by-Step Example: 996 = 108 + (n – 1) × 12
Understanding the Formula: How to Solve for n Using L = a + (n – 1)d
With Step-by-Step Example: 996 = 108 + (n – 1) × 12
When it comes to arithmetic progressions, one of the most useful formulas is:
Understanding the Context
L = a + (n – 1)d
Where:
- L = the last term in the sequence
- a = the first term
- n = the number of terms
- d = the common difference between successive terms
This formula is essential for solving word problems involving sequences, financial calculations, or mathematical progressions. In this article, we’ll break down how to use this formula, walk through a practical example—such as solving 996 = 108 + (n – 1) × 12—and explain how you can apply it to similar problems.
Image Gallery
Key Insights
What Does the Formula Mean?
The formula L = a + (n – 1)d describes how each term in an arithmetic sequence progresses. Starting from the first term a, each subsequent term increases (or decreases) by a constant d. The expression (n – 1)d calculates the total increment over n – 1 steps.
Applying the Formula: Step-By-Step Example
Let’s solve the equation step-by-step:
🔗 Related Articles You Might Like:
📰 You Wont Believe What Nextraqs Hidden Feature Does—Shocked Everyone! 📰 Nextraq just dropped the bombshell—Inside Its Revolutionary Technology Revealed! 📰 This Nextraq Reveal Is Changing Everything—Dont Miss It Before It Disappears! 📰 This Average Of An Average Method Drops Your Spreadsheet Confusionreportedly Used By Experts 9662706 📰 Podd Ticker 5576635 📰 Loop Noise Cancelling 4458517 📰 Arizona Raised 982694 📰 American Airlines Federal Credit Union Beat Mortgage Rates Like Never Before 9117457 📰 How To File Taxes 164574 📰 41670A Public Health Researcher Is Analyzing Data From Three Low Income Neighborhoods The Neighborhoods Have Populations Of 12000 18000 And 24000 Respectively If 15 Of The First 20 Of The Second And 25 Of The Third Residents Suffer From Uncontrolled Hypertension What Is The Overall Percentage Of Residents With Uncontrolled Hypertension Across All Three Neighborhoods 2514834 📰 Wells Fargo Brookhaven 9879113 📰 This Iot Internet Of Things Demo Will Shock Youheres Why Its The Most Important Tech Trend Of Our Time 7945178 📰 Point And Figure Chart 6327190 📰 You Wont Handle This Red Lingerie Without Turning Heads And Feeling The Heat 7992880 📰 You Wont Believe What Happened In The Heart Of Nebraskas Deadliest Game 5613597 📰 Hold Fast Meaning 6727992 📰 Pick A Side Roblox 4848783 📰 1906 Earthquake 8985909Final Thoughts
Given:
996 = 108 + (n – 1) × 12
This represents an arithmetic sequence where:
- L = 996 (the final term)
- a = 108 (the first term)
- d = 12 (the common difference)
- n = the unknown (number of terms)
Step 1: Isolate the term containing n
Subtract the first term from both sides:
996 – 108 = (n – 1) × 12
888 = (n – 1) × 12
Step 2: Divide both sides by 12
888 ÷ 12 = n – 1
74 = n – 1
