SOLUTION: The three numbers n-2, n, n+3, are consecutive terms of a geometric progression. i) Find n and the term after n+3

Question 1177530: The three numbers n-2, n, n+3, are consecutive terms of a geometric progression.
i) Find n and the term after n+3
Answer by ikleyn(52796) (Show Source): You can put this solution on YOUR website!
.


From the condition, you have this equation


    (n-2)*(n+3) = n^2.


Simplify


    n^2 + n - 6 = n^2

          n     = 6.     


So, n = 6;  the first three terms are  4, 6, 9,  and the next term is   =  =  =   = 13.5.     ANSWER

Solved.

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On geometric progressions, see the lessons

On geometric progressions, see introductory lessons
    - 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 (*)
in this site, and ESPECIALLY the lesson marked (*) in the list.

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.

...............

Do not forget to post your "THANKS" to me for my teaching.

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