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:

📰 9x6 Revolutionized This Industry—Find Out How Before It’s Too Late! 📰 Discover the Hidden Power of the 9th House Astrology – You Won’t Believe What It Reveals About Your Destiny! 📰 The 9th House Astrology Secret That Could Change Your Life – Stop Ignoring This Powerful Part of Your Chart! 📰 See How To Turn Any Text Into Numbers Insanely Simple Excel Hack 8969857 📰 Are You Ready Jynx Reveals The Ultra Moon Qr Code You Cant Ignore 8817085 📰 Japanese Occupation Of Korea 3050793 📰 Sql Server Report Services Unlock Hidden Insights Fastwatch Results Hit Instantly 3161346 📰 Disney Plus Begin Uncovered Hidden Feature Sets That Changed Everything 5548896 📰 Changing Region Got Me Banned Fortnite 1945121 📰 Roblox Classic Shirt Template Maker 📰 Song From Sinner 8900359 📰 Call Epic Games Support 📰 Squid Game Online Explodes In Popularitydownload Now For Mind Blowing Online Survival Action 3071199 📰 King Harald 8206707 📰 This Secret Benimaru Shinmon Trick Is Taking The Gaming World By Storm 5605830 📰 Smt V Steam 📰 Leslie Thompkins 📰 Police Confirm Us Market Today And It Sparks Debate

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