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Geometric & harmonic progressions formulas
8 formulas for Geometric & harmonic progressions, from the Algebra section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| GP n-th term | aₙ = a·rⁿ⁻¹ 🧮 Solve step by step | r common ratio |
| GP sum | Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1 🧮 Solve step by step | |
| Infinite GP | S∞ = a / (1 − r), |r| < 1 | |
| Geometric mean | G = √(ab) 🧮 Solve step by step | |
| Harmonic progression | 1/a, 1/(a+d), 1/(a+2d), … | reciprocals form an AP |
| Harmonic mean | H = 2ab / (a + b) 🧮 Solve step by step | |
| AM–GM–HM relation | A ≥ G ≥ H and G² = AH | positive a, b |
| AGP sum (infinite) | a/(1 − r) + dr/(1 − r)² | |r| < 1 |
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