General Term Calculator
Verified Calculation Engine
The online General Term Calculator helps you calculate instantly and solve problems related to Binomial Theorem. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Finds the (r+1)th term (general term) in binomial expansion: T(r+1) = nCr a^(n-r) b^r.
T(r+1) = nCr a^(n-r) b^r
General term formula for (r+1)th term in expansion of (a+b)^n
General term gives any specific term in the expansion
Inputs
Results
Worked Examples
Example 1: Basic
Find 3rd term in (x + y)^5
- a: 1
- b: 1
- n: 5
- r: 2
- term: 10x³y²
- coefficient: 10
- formula: T(3) = 5C2 x³ y² = 10x³y²
Example 2: Board Level
Find 4th term in (2x - 3y)^6
- a: 2
- b: -3
- n: 6
- r: 3
- term: -4320x³y³
- coefficient: -4320
- formula: T(4) = 6C3 (2x)³ (-3y)³ = -4320x³y³
About this calculator
Overview
General Term Calculator evaluates General Term for the math / binomial-theorem library. Primary input cue: First Term a [required]: First term. Method anchor: T(r+1) = nCr a^(n-r) b^r General term formula for (r+1)th term in expansion of (a+b)^n. General term gives any specific term in the expansion.
When to use
Use General Term Calculator when you already know the inputs and need general term without setting up a spreadsheet.
Inputs explained
- First Term a [required]: First term
- Second Term b [required]: Second term
- Power n [required]: Power
- Term Index r [required]: Index of term (0 to n)
Formula / method
T(r+1) = nCr a^(n-r) b^r General term formula for (r+1)th term in expansion of (a+b)^n. General term gives any specific term in the expansion (calculator id: general-term-calculator).
Worked example
Worked values: a = 1, b = 1, n = 5, r = 2 → term = 10x³y², coefficient = 10, formula = T(3) = 5C2 x³ y² = 10x³y²
Interpreting results
Read the primary output as general term under the method on this page.
Assumptions
- Inputs for `general-term-calculator` follow the on-page labels; values/shapes must match this operation.
- Units (when shown) must be consistent across inputs for general term.
- Real-number arithmetic is used unless general term explicitly needs integers.
Limitations
- General Term Calculator cannot invent missing inputs; incomplete forms stop short of a forged general term value.
- Display rounding can differ slightly from a CAS/symbolic exact form of general term.
- Complex/branch cuts and undefined points are not always interactively annotated for general term.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
T(r+1) = nCr a^(n-r) b^r General term formula for (r+1)th term in expansion of (a+b)^n. General term gives any specific term in the expansion (calculator id: general-term-calculator).
Example Calculation
Worked values: a = 1, b = 1, n = 5, r = 2 → term = 10x³y², coefficient = 10, formula = T(3) = 5C2 x³ y² = 10x³y²
Frequently Asked Questions
What is General Term Calculator?
- General Term Calculator evaluates General Term for the math / binomial-theorem library. Primary input cue: First Term a [required]: First term. Method anchor: T(r+1) = nCr a^(n-r) b^r General term formula for (r+1)th term in expansion of (a+b)^n. General term gives any specific term in the expansion.
How does General Term Calculator work?
- T(r+1) = nCr a^(n-r) b^r General term formula for (r+1)th term in expansion of (a+b)^n. General term gives any specific term in the expansion (calculator id: general-term-calculator).
Why use this Math Numbers calculator?
- Use General Term Calculator when you already know the inputs and need general term without setting up a spreadsheet.