Question

relation among HP GP and AP​

Answer 1

Answer:

Relation Between AP, GP and HP

Progression also known as sequence or series, are the types of numbers which are placed in a particular order to form a recognizable table. Simply we can say that harmonic progression is the reciprocal of the values of the terms in arithmetic progression. It can be explained as if the terms of arithmetic progression like a, b, c, d, e, f are available in the form of 1/a, 1/b, 1/c, 1/d, 1/e, 1/f, in which terms of harmonic progression can be written as 1/a, 1/(a + d), 1/(a + 2d), etc. A sequence can be said in harmonic progression only when the terms are in harmonic mean with their neighboring terms.

 Harmonic mean is to find out the average speed of the journey where the average formula of the speed can be given by 2ab/ (a + b) kmph, where a and b are the speed at which a person travels a distance of A and B. Harmonic mean can be easily calculated with the help of the following example;

If three terms a, b and c are in harmonic progression then, the terms in arithmetic progression include 1/a, 1/b, 1/c,

• 2/b = 1/a + 1/c

• b = 2ac/ (a + c)

In the above equation, b is the harmonic mean of its other two neighboring terms (a, c).

Conditions to solve the terms of harmonic progression:

Answer 2

Answer:

Let GP be G

HP be H

AP be A

Now,

G^2=A×H

G=✓A×H

As the three are in geometric progression with each other.