.
Since a, a-12 and a+12 are three consecutive terms of an geometric progression, you have
= . ( the ratio is the same as the ratio )
Then cross-nultiplying
= a*(a+12) ====>
a^2 - 24a + 144 = a^2 + 12a ====>
-24a + 144 = 12a ====> 144 = 24a + 12a ====> 144 = 36a ====> a = = 4.
Your GP is 4, 4-12 = -8, 4+12 = 16.
It has the first term 4 and the common difference (-2).
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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 part of this online textbook under the topic "Geometric progressions".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.