Geometric Progression (G.P.): A geometric progression (G.P.) is a sequence of numbers such that the ratio of consecutive numbers is constant. This constant...
Geometric Progression (G.P.):
A geometric progression (G.P.) is a sequence of numbers such that the ratio of consecutive numbers is constant. This constant ratio can be positive or negative, and it determines the growth or decay of the sequence.
Definition:
A geometric progression is a sequence of numbers such that the ratio of consecutive numbers is constant.
This constant ratio can be positive or negative.
Examples:
1, 2, 4, 8, 16, 32
1, 2, 4, 8, 16, 32, 64
Properties of G.P.:
The common ratio of a G.P. is always constant.
A G.P. follows a specific order of numbers.
The sum of any finite G.P. is equal to the product of its first and last numbers divided by the constant ratio.
Applications of G.P.:
Geometric progressions have diverse applications in various fields, including mathematics, physics, and finance.
They are used to model real-world phenomena, such as population growth, decay of radioactive materials, and geometric sequences.
Geometric progressions are essential in the study of arithmetic and geometric sequences and series