SOLUTION: Consider a geometric sequence whose third term is 9 and whose sixth term is −8/3. What is its first term? (Enter a number only)

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Question 1091771: Consider a geometric sequence whose third term is
9 and whose sixth term is −8/3. What is its first term?
(Enter a number only)

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
a%5B3%5D = 9 = a%2Ar%5E2,

a%5B6%5D =-8%2F3 = a%2Ar%5E5,


==========>  a%5B6%5D%2Fa%5B3%5D = 9%2F%28%28-8%2F3%29%29 = %28a%2Ar%5E5%29%2F%28a%2Ar%5E2%29 = r%5E3

==========>  r%5E3 = -%289%2A3%29%2F8 = -27%2F8

==========>  r = root%283%2C+%28-27%2F8%29%29 = -3%2F2


==========>  9 = a%2Ar%5E2 = a%2A%28-3%2F2%29%5E2 = a%2A%289%2F4%29

==========>  a = 9%2F%28%289%2F4%29%29 = 4.


Answer.  a = a%5B1%5D = 4.

SOLVED.


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On geometric progressions see the 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
    - 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
in this site.

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

https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Consider a geometric sequence whose third term is
9 and whose sixth term is −8/3. What is its first term?
(Enter a number only)
highlight_green%28matrix%281%2C3%2C+First%2C+%22term%3A%22%2C+20.25%29%29