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:

📰 When Does Sonic 4 Release? The Surprising Countdown You Won’t Believe! 📰 3! Samsung’s Countdown Has Begun: Sonic 4 Release Date Finally Revealed! 📰 Sonic 4 Shocked Fans—The Exact Date You’ve Been Waiting For! 📰 The Truth About Oliver Mcqueen Why Every Creative Deserves A Tribute 📰 The Truth About Orka Will Change Everything You Think You Know 📰 The Truth About Papa Papa Louie Powder Keg Moments Everyones Talking About 📰 The Truth About Para That Is Definitely Hiding From Tourists 📰 The Truth About The Norwegian Flag Why This Simple Design Holds Deep Cultural Power 📰 The Truth Behind The Icon Olivia Wildes Leaked Nudes Blow Your Minddont Miss 📰 The Truth Is Our Faultwatch As Consequences Unfold Immediately 📰 The Ultimate Breakdown Of O2 Lewis Structure You Wont Believe How It Works 📰 The Ultimate Breakdown Untold Facts About Ouran Host Club Characters Youve Been Missing 📰 The Ultimate Chronological Journey Through The Order Of Star Wars Movies You Cant Miss 📰 The Ultimate Classic Dive Into Every Legendary Detail Of Ouran Highschool Club Characters 📰 The Ultimate Collection Of Nintendo Switch 2 Platform Games You Need To Play 📰 The Ultimate Guide Perfect Page Numbers That Make Books More Magical 📰 The Ultimate Guide The Hidden Order Of Fast Furious Movies You Need To Know Now 📰 The Ultimate Guide To Confidence Master The Panty And Stocking With Garterbelt Look

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