Math Formulas

Arithmetic Sequence Formulas

Find the nth term and sum of an arithmetic sequence. Formulas: aₙ = a₁ + (n-1)d and S = n/2 × (a₁ + aₙ) with worked examples.

Combinations Formula

Calculate the number of ways to choose items with C(n,r) = n! / (r!(n-r)!). Learn when order does not matter in counting problems.

Distance Formula

Calculate the distance between two points in a coordinate plane using the distance formula d = √((x₂-x₁)² + (y₂-y₁)²). Includes step-by-step examples.

Exponent Rules

Complete guide to exponent rules: product, quotient, power, zero, and negative exponents. Simplify expressions with these essential rules.

Factorial Formula

Calculate n factorial (n!) — the product of all positive integers from 1 to n. Used in permutations, combinations, and probability.

Geometric Sequence Formulas

Find the nth term and sum of a geometric sequence. Formulas: aₙ = a₁ × r^(n-1) and S = a₁(1-rⁿ)/(1-r) with worked examples.

Logarithm Properties

Essential logarithm rules including product, quotient, power, and change of base. Learn how to simplify and solve log expressions.

Midpoint Formula

Find the exact midpoint between two points using M = ((x₁+x₂)/2, (y₁+y₂)/2). Step-by-step examples and explanation.

Percentage Formula

Calculate percentages using Percentage = (Part / Whole) × 100. Includes formulas for percentage increase, decrease, and finding the whole.

Permutations Formula

Calculate the number of ordered arrangements with P(n,r) = n! / (n-r)!. Learn when order matters in counting problems.

Quadratic Formula

The quadratic formula solves any equation of the form ax² + bx + c = 0. Find both roots instantly with this essential algebra formula.

Slope Formula

Calculate the slope of a line between two points using m = (y₂-y₁)/(x₂-x₁). Learn what slope means with worked examples.