.
To prove that the sequence is a geometric progression, consider the ratio .
Since is an AP, you have = , where d is the common difference of the AP, i.e. the constant term independent on "n'.
Therefore, = = = .
Thus the ratio of two consecutive terms and is the constant value .
By the definition, it means that the sequence is a geometric progression.
The proof is completed.
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There is a bunch of lessons on arithmetic progressions in this site:
- Arithmetic progressions
- The proofs of the formulas for arithmetic progressions
- Problems on arithmetic progressions
- Word problems on arithmetic progressions
- Mathematical induction and arithmetic progressions
- One characteristic property of arithmetic progressions
- Solved problems on arithmetic progressions
There is a bunch of lessons on geometric progressions in this site
- Geometric progressions
- The proofs of the formulas for geometric progressions
- Problems on geometric progressions
- Word problems on geometric progressions
- One characteristic property of geometric progressions
- Solved problems on geometric progressions
- Fresh, sweet and crispy problem on arithmetic and geometric progressions
- Mathematical induction and geometric progressions
- Mathematical induction for sequences other than arithmetic or geometric
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the parts of this online textbook under the topics "Arithmetic progressions" and "Geometric progressions".
Save the link to this textbook
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.