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| Relation between AM, GM , HM For two positive numbers a and b A = Arithmetic mean =(a+b)/2 G = Geometric Mean = Sqrt(ab) H = Harmonic Mean =2ab(a+b) Multiplying A and H, we get A x H = {(a+b)/2}*{2ab/(a+b)} =ab =G^2 NOTE : AM >= GM >= HM |
| A series of quantities is said to be in a harmonic progression when their reciprocals are in arithmetic progression. Example : 1/3,1/5,1/7....and 1/a,1/(a+d), 1/(a+2d).....are in HP as their reciprocals 3, 5, 7, …, and a, a + d, a + 2d….…. are in AP. T(n) of the HP is =1/{a+(n-1)d} In order to solve a question on HP, one should form the corresponding AP. |
