Arithmetic Progressions

An AP is a sequence where

An AP is a sequence where each term after the first is obtained by adding a constant value (common difference) to the previous term. Example: 2, 5, 8,

The fixed number added to each

The fixed number added to each term to get the next term. Formula: d = aₖ₊₁ - aₖ. Can be positive (increasing AP), negative (decreasing AP), or zero (

aₙ = a + (n

aₙ = a + (n-1)d, where a is first term, d is common difference, n is term number. Step-by-step application: 1) Identify a and d, 2) Substitute values,

Two formulas

Two formulas: Sₙ = n/2[2a + (n-1)d] or Sₙ = n/2(first term + last term). Method: 1) Use first formula when a, d, n are known, 2) Use second when first

If three numbers

If three numbers a, b, c are in AP, then b = (a+c)/2 (b is arithmetic mean). APs appear in: salary increments, loan calculations, construction measure