Question

What is the relation between AP, GP, and HP?

Answer 1

Arithmetic Progression

• An arithmetic progression (AP) is a sequence of numbers in which each succeeding number is obtained either by adding or subtracting a specific number called the common difference.
• The general form of AP is: $a,a+d,a+2d,....$ , where $d$ is the common difference.

Geometric Progression:

• A geometric progression (GP) is a sequence of numbers in which each succeeding number is obtained by multiplying a specific number called the common ratio.
• The general form of GP is: $a,ar,a{r}^2,....$ , where $r$ is the common ratio.

Harmonic Progression:

• A sequence of numbers is said to be a harmonic progression if the reciprocal of those numbers are in AP.
• The general form of HP is: $\frac{1}{a},\frac{1}{a+d},\frac{1}{a+2d},....$

The relation between AP, GP, and HP is,

${\left(GP\right)}^2=\left(AP\right)\times \left(HP\right)$