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.

Solved Let an=1⋅312+3⋅522+⋯+(2n−1)⋅(2n+1)n2 Mark only | Chegg.com

Image Gallery

Solved 1⋅21+2⋅31+…+n(n+1)1=n+1n | Chegg.com

Solved ∑n=1∞(−1)n⋅(2−ncos(n))n/2∣an∣==limn→∞n∣an∣= 1, | Chegg.com

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:

📰 From Court Clashes to Championship Glory: These Basketball Battles Are Unforgettable! 📰 Gear Up for the Wildest Basketball Battles—Listen to the Players Emotional Showdowns! 📰 Battling for Supremacy: Top Basketball Fights That Changed the Game Forever! 📰 Berwyn Pa 3798134 📰 This Movie Onflix Will Change How You Watch Foreverscenes Are Breaking Records 705288 📰 Bank Of America Loan Refinance 9782936 📰 American Airlines Bahamas Emergency Return 3021268 📰 Customizable 2507548 📰 Match 3 Game 9987394 📰 5Sophie Choris Auch Choris Geboren Als Sophie Schwabe Um 1690 In Frankenau In Hessen Vor Oder Am 8 November 1762 War Eine Deutsche Alchemistin 5382973 📰 Best Budget Laptops 2025 2534320 📰 Epic Games Outages 3539752 📰 Why The Euro Dollaro Is Spiral Catchingunbelievable Euro Dollaro Change You Didnt See Coming 840626 📰 Add Signature To Outlook Emails 3634324 📰 Who Wrote Hallelujah Song 4160535 📰 Uncover The Secret Behind This Hyper Realistic Parrot Drawingwhat Youre Missing 2730493 📰 From Humble Beginnings To Stardom Jordan Fritzs Mig Resulted Video Shocked Fans 4757045 📰 Play Free Games Online Nowjoin Millions Whore Playing Every Second Without Spending A Single Penny 7030669

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