Question

What are AP, GP, and HP?

Answer 1

Step-1: Arithmetic Progression (AP):

• Arithmetic progression is a sequence of numbers in which the difference between any two consecutive numbers is a constant value.
• The constant value is called a common difference.
• The general form of an AP: $a,a+d,a+2d,a+3d,.....$ , where $a$ is the first term and $d$ is a common difference

Step-2 : Geometric Progression (GP):

• A geometric progression is a sequence in which each consecutive element is obtained by multiplying the preceding element by a constant.
• The constant value is called a common ratio.
• The general form of an AP: $a,ar,a{r}^2,a{r}^3,.....$ , where $a$ is the first term and $r$ is a common ratio.

Step-3: Harmonic Progression (HP):

• A harmonic progression is a sequence of real numbers which is determined by taking the reciprocals of the arithmetic progression that does not contain $0$.
• The general form of HP: $\frac{1}{a},\frac{1}{a+d},\frac{1}{a+2d},\frac{1}{a+3d},....$