AP properties include relationships between terms: (1) If a, b, c in AP, then 2b = a + c (arithmetic mean); (2) Sum of equidistant terms from ends = constant. For AP a, a+d, a+2d, ..., aₙ: first + last = a₂ + aₙ₋₁ = a₃ + aₙ₋₂, etc.; (3) Inserting arithmetic means: If k means inserted between a and b, common difference = (b-a)/(k+1); (4) Three numbers in AP: Express as a-d, a, a+d. Example: Numbers summing to 15 in AP. Let a-d, a, a+d. Sum = 3a = 15 → a = 5. If product = 105, (5-d)(5)(5+d) = 105 → 5(25-d²) = 105 → d = 2. Numbers: 3, 5, 7. Exam tip: Use properties to solve problems without finding all terms. Practice: Insertion and identification problems.