l = a + (n-1)d \implies 996 = 108 + (n-1) \cdot 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.

$l = a + (n-1)d \implies 996 = 108 + (n-1) \cdot 12$

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:

📰 Step Into Legend of Zelda A Link to the Past Walkthrough — This Hidden Secret Will Blow Your Mind! 📰 You’re Crazy… This Legend of Zelda Walkthrough Has the Past Appearing Over and Over — Try It Now! 📰 A Link to the Past Mastery Walkthrough on SNES — Look Away Before You Forget the Secrets! 📰 This Soldier Field Seating Layout Changed Spectator Strategy Forever 📰 This Soldier Meme Wont Let You Breathe Youve Got To See Whats Inside 📰 This Soldiers Fire 📰 This Solgaleo Hack Will Take Your Pokmon Go Gameplay To The Next Level 📰 This Solid Black Item Will Transform Your Look Overnight Shocking Disezn 📰 This Solid Snake Big Boss Battle Will Blow Your Mindsee Why Gamers Are Obsessed 📰 This Solid Snake Will Change How You Fight You Wont Believe Its Power 📰 This Solid Wood Coffee Table Will Transform Your Living Roomcheck It Out Before It Sells Out 📰 This Solid Wood Dining Room Table Is The Ultimate Statement Piece For Every Home 📰 This Solid Wood Dresser Is So Stylish Youll Forget About Cheap Furniture Forever 📰 This Soliloquiando Moment Changed Everythingsee Who Was Left Speechless 📰 This Solitaire Engagement Ring Is The Secret To Your Forever Lovediscover It Now 📰 This Solo Leveling Main Character Beat Legionary Arms Witness The Unstoppable Climax 📰 This Solo Leveling Reawakening Movie Moment Will Change How You See Virtual Worlds Forever 📰 This Somebody Like You Kings Of Leon Lyrics Will Shock Youyoure Not Ready For This

Final 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