GP properties: (1) If a, b, c in GP, then b² = ac (geometric mean); (2) Sum of equidistant terms from ends = constant ratio product. For GP a, ar, ar², ..., arⁿ⁻¹: first × last = second × second-last = ar × ar^(n-1) = a²r^n; (3) Inserting geometric means: If k means inserted between a and b, common ratio = (b/a)^(1/(k+1)); (4) Three numbers in GP: Express as a/r, a, ar. Example: Numbers with sum 14 in GP. Let a/r, a, ar. Sum = a(1/r + 1 + r) = 14. If product = 64, (a/r)(a)(ar) = a³ = 64 → a = 4. Then 4(1/r + 1 + r) = 14 → r = 2 or 1/2. Numbers: 2, 4, 8 or 8, 4, 2. Exam tip: Use geometric mean to check GP. Practice: Complex GP problems.