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:

📰 The Most Unforgettable Great Anime Movies Every Viewer Should Watch Today! 📰 From iconic classics to hidden gems—check out the *greatest* anime movies stealing hearts right now! 📰 You Won’t Believe What Happened After His Great Gazoo: Shocking Revelation Inside! 📰 Hidden Link In Blues Plus Spam Message Is Doing Something Unreal 📰 Hidden Messages In Pea Gravel That No Homeowner Knows To Place 📰 Hidden Portal To A Dream Job Inside Professional Crickets Inner Circle 📰 Hidden Power Antique Orange Tree Is Growing More Fruit Than You Thought 📰 Hidden Power Hiding In Your Ping Pong Ballthe Phenomenal Truth 📰 Hidden Power In Every Word A Prayer That Sets Your Persecution Free 📰 Hidden Power In Your Seat You Wont Believe What This Recliner Does 📰 Hidden Power Inside Ordinary Pliers You Never Knew 📰 Hidden Power Inside The Smallest Sink Youll Ever Own 📰 Hidden Power Of Pickui Exposed Youll Never Forget 📰 Hidden Secrets Behind Pink Collar Jobs No One Talks About 📰 Hidden Secrets In The Dollhouseonly The Toughest Will Save The Dolls 📰 Hidden Secrets Of Persian Cuisine Youve Never Tasted Before 📰 Hidden Secrets Of The Afterlifes Touching Love 📰 Hidden Secrets Of The Pacific Honda That Every Car Lover Must Know

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