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:

📰 Ending of The Last of Us: Joel’s Death Sparks What Fans Were Too Shocked To Expect! 📰 You Won’t Believe This PS5 Gamer’s PS4 Controller Setup Shocked the Internet! 📰 Does Your PS4 Controller Work on PS5? The Surprising Truth You Need to Know 📰 Shocking Fortnite Memes Youve Seen Or Needed Later Ready To Discover Them 📰 Shocking Fortnite Screenshots Youve Been Huntingview The Ultimate Collection 📰 Shocking Fortnite Survey Skins You Needwe Tested Limitless Collection Today 📰 Shocking Fox Terrier Hair Why Every Dog Lover Wants This Fur In 2024 📰 Shocking Fragrance Flavor In Every Sip Fruit Alcohol Cocktail Hack Revealed 📰 Shocking Free Black Porn Sites List Watch Download And Enjoy For Free Now 📰 Shocking French Curse Words Thatll Make You Say Bon Dieu Out Loud 📰 Shocking French Manicure Designs That Are Taking Social Media By Storm 📰 Shocking French Nails That Suddenly Made Every Outfit Shine 📰 Shocking Friendsgiving Food Ideas Thatll Blow Your Holiday Dinner Away 📰 Shocking Front Door Colors That Avoid Common Mistakesboost Curb Appeal Instantly 📰 Shocking Front Door Decor Ideas That Will Transform Your Homes First Impression 📰 Shocking Fruit Battlegrounds Revealed Whos Winning The Ultimate Produce Showdown 📰 Shocking Fruit Platter Ideas Your Kitchen Will Demand Online 📰 Shocking Fruits List Everyone Should Knowyou Wont Believe Whats In It

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