Arithmetic Progressions

An AP is a sequence where

An AP is a sequence where each term is obtained by adding a fixed number (common difference) to the previous term. Examples: 2, 5, 8, 11, ... (d = 3);

Common difference d = aₙ₊₁

Common difference d = aₙ₊₁ - aₙ for any term. For example, in AP 3, 7, 11, 15: d = 7-3 = 4, or d = 11-7 = 4. Always subtract the earlier term from the

The formula aₙ = a +

The formula aₙ = a + (n-1)d gives any term in the AP. Step-by-step application: (1) Identify first term 'a', (2) Find common difference 'd', (3) Subst

Two formulas

Two formulas: S = n/2[2a + (n-1)d] when first term and common difference are known, and S = n/2(a + l) when first and last terms are known. Derivation

If

If a, b, c are in AP, then b = (a+c)/2, meaning the middle term is the arithmetic mean of the other two. This property helps solve problems where term