Answer :
There is indeed a geometric relationship between the elements of a progression, specifically in a geometric progression (GP). In a geometric progression, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
For example, in a GP with a first term of 'a' and common ratio 'r', the terms of the progression would be:
1. First term: a
2. Second term: ar
3. Third term: ar^2
4. Fourth term: ar^3
5. And so on...
The relationship between consecutive terms in a geometric progression is that each term is obtained by multiplying the preceding term by the common ratio 'r'. This relationship remains consistent throughout the progression.
This geometric relationship distinguishes a geometric progression from an arithmetic progression, where the terms are generated by adding a fixed number to the preceding term.
For example, in a GP with a first term of 'a' and common ratio 'r', the terms of the progression would be:
1. First term: a
2. Second term: ar
3. Third term: ar^2
4. Fourth term: ar^3
5. And so on...
The relationship between consecutive terms in a geometric progression is that each term is obtained by multiplying the preceding term by the common ratio 'r'. This relationship remains consistent throughout the progression.
This geometric relationship distinguishes a geometric progression from an arithmetic progression, where the terms are generated by adding a fixed number to the preceding term.
