l = a + (n-1)d \implies 996 = 108 + (n-1) \cdot 12 - Sterling Industries
Understanding the Formula: How to Solve for n Using L = a + (n – 1)d
With Step-by-Step Example: 996 = 108 + (n – 1) × 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.
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:
📰 Yes, Our Health Department Just Cracked Down—Heres Whats Really Going on in America! 📰 Health Savings Account Explained: Unlock Massive Savings Youve Been Ignoring! 📰 This Simple Health Savings Account Guide Will Save You Thousands—Dont Miss It! 📰 Bond James Spectre 📰 Orileys Auto Parts Stock 976019 📰 Free Skins In Fortnite 📰 Cryptocurrency Wallet Best 📰 Verizon Policy On Upgrades 📰 Roblox Scipt 📰 Why Sunset Orange Is Taking Over Social Media This Fallyou Have To See It 3775816 📰 Clicker Poop 4349965 📰 Wordle Hint Nov 4 📰 Turbo Vpn Free Download For Pc 📰 To The Zero Power 📰 Boa Credit Card Customer Service 📰 Sledding Game Steam 📰 Thomas Moore Clinic 📰 Lowest Mortgage Interest Rates TodayFinal 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
