Question

What is a Progression?

Answer 1

Progression: Progression is a list of numbers that exhibit a particular pattern.

Three types of Progression:

• Arithmetic progression: 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.

Example: $1,3,5,7,9,....$ is a geometric progression with a common difference $2$.

• Geometric progression: A geometric progression is a sequence in which each consecutive element is obtained by multiplying/divide the preceding element by a constant. The constant value is called a common ratio.

Example: $1,3,9,27,81,....$ is a geometric progression with a common ratio $3$.

• Harmonic progression: A harmonic progression is a sequence of real numbers which is determined by taking the reciprocals of the arithmetic progression that does not contain $0$.

Example: $1,\frac{1}{2},\frac{1}{3},\frac{1}{4},....$ is a harmonic progression. Reciprocal of each term of the sequence form an arithmetic progression.