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Algebra
High School
Algebra (High School Level)
Geometric Progression - nth Term
Find the nth term of a geometric progression
Standard Formula
aₙ = a × r⁽ⁿ⁻¹⁾
Interactive Sandbox
Live Reactive
Adjust values in real-time and observe mathematical cause-and-effect
a
120
r
120
n
120
Live EquationFormula Proof
2 ₙ = 2 × 3⁽ⁿ⁻¹⁾ = 162
m = 1.5b = 1
Calculated Solution
162
Direct computational model evaluating Geometric Progression - nth Term.
Variable Mechanics
Roles, constraints & impacts
3 Params
a
First Term
First Term
ImpactPrimary formula parameter
ConstraintReal number
r
Common Ratio
Common Ratio
ImpactPrimary formula parameter
ConstraintReal number
n
Term Number
Term Number
ImpactPrimary formula parameter
ConstraintReal number
At a Glance
Gotchas, units & real-world use
Essential
Formula Nature & Mechanics
Direct computational model evaluating Geometric Progression - nth Term.
Common Mistakes & Traps
- Ensure all input measurements share consistent units before calculating.
- Check for denominator values approaching zero to prevent undefined division.
- Follow standard order of operations (PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract).
Dimensional Analysis & Units
Direct evaluation matching formula variable dimensions.
Real-World & Industry Application
Widely utilized across modern algebra applications, academic analysis, and engineering estimations.
Worked Example: Geometric Progression - nth Term
Given:
- a = 2
- r = 3
- n = 5
- aₙ = a × r⁽ⁿ⁻¹⁾
- a₅ = 2 × 3⁴
- a₅ = 2 × 81
- a₅ = 162
Answer: 162
Frequently Asked Questions
What is the Geometric Progression - nth Term formula?
aₙ = a × r⁽ⁿ⁻¹⁾. Find the nth term of a geometric progression.
How do I calculate Geometric Progression - nth Term?
Enter First Term (a), Common Ratio (r), Term Number (n) into the calculator. It applies aₙ = a × r⁽ⁿ⁻¹⁾ and shows every step of the working.
Related Algebra Calculators
Quadratic Formulax = (-b ± √(b² - 4ac)) / 2aSlope Formulam = (y₂ - y₁)/(x₂ - x₁)Simultaneous Equations Solvera₁x + b₁y = c₁ ; a₂x + b₂y = c₂Arithmetic Progression - nth Termaₙ = a + (n - 1)dArithmetic Progression - SumSₙ = n/2 × [2a + (n - 1)d]Geometric Progression - SumSₙ = a(rⁿ - 1) / (r - 1)
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