f(1) = 15,\quad f(2) = 30,\quad f(3) = 45,\quad f(4) = 60 - Malaeb
Understanding the Linear Pattern: Solving for f(n) = 15 at f(1) = 15, f(2) = 30, f(3) = 45, f(4) = 60
Understanding the Linear Pattern: Solving for f(n) = 15 at f(1) = 15, f(2) = 30, f(3) = 45, f(4) = 60
When examining a sequence of ordered pairs such as:
- f(1) = 15
- f(2) = 30
- f(3) = 45
- f(4) = 60
Understanding the Context
we notice a clear arithmetic progression: each term increases by 15 as the input increases by 1. This strong linear pattern suggests that the function f(n) is linear in nature, describable by a simple equation of the form:
f(n) = an + b, where a is the slope and b is the y-intercept.
Step 1: Confirming the Linear Relationship
Let’s plug in values to find a and b.
Using f(1) = 15:
a(1) + b = 15 → a + b = 15 (1)
Image Gallery
Key Insights
Using f(2) = 30:
a(2) + b = 30 → 2a + b = 30 (2)
Subtract (1) from (2):
(2a + b) − (a + b) = 30 − 15
a = 15
Substitute a = 15 into (1):
15 + b = 15 → b = 0
Thus, the function is:
f(n) = 15n
Check with all points:
- f(1) = 15×1 = 15
- f(2) = 15×2 = 30
- f(3) = 15×3 = 45
- f(4) = 15×4 = 60
🔗 Related Articles You Might Like:
📰 bilateral hearing loss icd 10 📰 2000 honda civic cars 📰 lexus hybrid sedan 📰 5 Sango Shock The Forbidden Knowledge No One Is Talking About Dare To Discover 1075019 📰 1720 6900355 📰 Un Jardn Rectangular Que Mide 15 Metros Por 10 Metros Se Cubrir Con Mantillo Si Un Metro Cuadrado Requiere 3 Kilogramos De Mantillo Cuntos Kilogramos De Mantillo Se Necesitan En Total 4560080 📰 Following Fidelity 401 Heres What Could Be Changing Your Financial Future Forever 7712436 📰 A Climatologist Models Sea Level Rise And Predicts That By 2100 Sea Levels Will Rise By 05 Meters Over 80 Years If The Rate Of Rise Accelerates By 25 In The Last 30 Years What Was The Average Annual Rise During The Initial 50 Years 870021 📰 Hhs Just Blasted Major Security Gapsheres How Theyre Finally Fixing Them 6778497 📰 Inside The Secretary Of Healths Hidden Strategy To Save A Nation 2241217 📰 Dr Perky 4034376 📰 Watch Wicked Online Free 5187058 📰 You Wont Believe What Happens When Truth Or Dare Goes Viral 8520698 📰 5 How Lennar Stock Gained 50 In A Weekheres What You Cant Afford To Miss 3945064 📰 The Future Of Gaming Is Here Switch 2 Release Date Just Droppedheres How You Can Prepare 3657525 📰 5 Ntsk Stock Price Investors Are Locking In Millions Before Next Surprise Move 4137529 📰 Trash Icon Windows The Unlikely Trend Ruling Home Decor And Tech Spaces 439768 📰 The Righteous Gemstones Season 2 Dropsthis Gemstone War Will Blow Your Mind 6950877Final Thoughts
✓ Confirmed—this linear model fits perfectly.
Step 2: Real-World Meaning Behind the Pattern
Functions like f(n) = 15n model proportional growth, where the output increases steadily with the input. In practical terms, if f(n) represents a total value accumulating per time unit, then:
- After 1 unit: $15
- After 2 units: $30
- After 3 units: $45
- After 4 units: $60
This could represent an increasing bonus per hour, escalating rewards, or cumulative payments growing linearly with time.
Step 3: Predicting Future Values
Using the formula f(n) = 15n, you can easily compute future outputs:
- f(5) = 15×5 = $75
- f(6) = 15×6 = $90
This predictable growth makes linear functions ideal for modeling steady, consistent change.
Step 4: Alternative Representations
Though f(n) = 15n is the simplest form, the same sequence can also be expressed using recursive definitions:
- Recursive form:
f(1) = 15
f(n) = f(n−1) + 15 for n > 1
This recursive pattern mirrors the additive growth visible in the table.
