Harmonic progressions is formed by taking the reciprocals of an arithmetic progression.
So if you start with some number a, and add a common difference d each time, the arithmetic progression would be a, a+d, a+2d, a+3d etc.
The harmonic progression comes from taking the reciprocals of these terms.
So we have a, a/(1+d), a/(1+2d), a/( 1+3d)...
Here is a harmonic progression: 1/6, 1/4, 1/3, ....
1) Pathway of a charged particle when it enters a magnetic field... 2) Pendulum oscillations. (simple harmonic motion)
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GEM Maths is for students who are very good at maths, who likely got a 5 in 5th Grade FCAT Maths assessment and who are willing to commit MANY hours of maths homework. If a student can't give this kind of time and effort than Advanced Math is better.