An Geometric progression is a list of numbers in which each term is obtained by multiplying or dividing a fixed number to the preceding term, except the first term.
This fixed number is called the common ratio of the GP.
Eg: 2, 4, 8, 16, . . . is a geometric progression as each term of it multiplied by 2 gives its next term. (Clearly, common ratio r = 2).
Properties of geometric progression
- The ratio between the consecutive terms of a G.P. is always the same.
- 2. In a G.P., the product of the two terms equidistant from its beginning and from its end is always constant which is equal to th eproduct of its first term and its last term.
- 3. If a, b and c are in G.P.
- 4. In a G.P., if the terms at equal distances are taken, these terms are also in G.P.
5. If each term of a G.P. be multiplied or divided by the same non-zero number, the resulting seriesm is also a G.P.
The series obtained by taking the reciprocals of the terms of a G.P., is also a G.P.
- If each term of a G.P. is raised to the same non-zero number, the resulting series is also a G.P.
- (i) IF the corresponding terms of two different G.P.s are multiplied together; the resulting series, so obtained. is also a G.P.
- (ii) In the same way, if terms of a G.P. be divided by corresponding terms of some other G.P., the resulting series, so obtained, is also a G.P.