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:

📰 This Cowboy Casserole Will Transform Your Dinner—Here’s How! #CowboyCookingMagic 📰 Fast, Familiar, and Fermented: The Perfectionist’s Cowboy Casserole Recipe Now! 📰 You’ll NEVER Guess How EASY It Is to Make Elite Cowboy Cookie Recipes! 📰 Jacksonville Jaguars Logo 4357300 📰 Salt Bar 2000558 📰 Hotels In The 6Th District Paris 9230647 📰 Get The Only Hot Tent Built To Keep You Comfort Locked All Night Long 1311016 📰 Palpatines Dark Legacy Revealed Everything About Darth Sidious Youve Missed 5298530 📰 Define Disciple 7650177 📰 Ingress Mmo 9324190 📰 Regal Cinemas Movies 753112 📰 Difference 1080000 480000 1080000 480000 600000600000 5268644 📰 Clementine Music 5121799 📰 Gina Waps Shocking Secret That Will Change How You See Her Forever 4398102 📰 Jason Isaacs White Lotus 137328 📰 Fu Hua Shocked Us All This Hidden Truth Will Blow Your Mind 1963544 📰 The Hitech Act 5874241 📰 Passion Vine 121077

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