SOLUTION: In a geometric sequence where the 3rd term is 18 and the 8th term is 4,374, find the nth term.

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Question 1100227: In a geometric sequence where the 3rd term is 18 and the 8th term is 4,374, find the nth term.
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.
a%5B3%5D = a%5B1%5D%2Ar%5E2,    (1)

a%5B8%5D = a%5B1%5D%2Ar%5E7.    (2)

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a%5B8%5D%2Fa%5B3%5D = 4374%2F18 = 243 = %28a%5B1%5D%2Ar%5E7%29%2F%28a%5B1%5D%2Ar%5E2%29 = r%5E5  ====>


r = root%285%2C243%29 = 3.


Thus the common ratio is 3.


Then the first term  is  a%5B1%5D = a%5B3%5D%2Fr%5E2 = 18%2F3%5E2 = 2.


Answer.  The first term  is 2.  The common ratio is  3.

         The n-th term is a%5Bn%5D = 2%2A3%5E%28n-1%29.

Solved.

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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
    - Solved problems on geometric progressions
    - Fresh, sweet and crispy problem on arithmetic and geometric progressions


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.