SOLUTION: The sum of first four terms of GP is 30 and that of the last four terms is 960. If the first and last term of GP are 2 and 512 respectively, find the common ratio.

Question 1062189: The sum of first four terms of GP is 30 and that of the last four terms is 960. If the first and last term of GP are 2 and 512 respectively, find the common ratio.
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
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The sum of first four terms of GP is 30 and that of the last four terms is 960. If the first and last term of GP
are 2 and 512 respectively, find the common ratio.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The sum of the first four terms is

S = .         (1)


The sum of the last four terms is

T =  =              (2)

  =  = 

  =           (2')

Now divide T by Q (divide (2') by (1)). You will get

 =  =  = ,   or

32 = ,   or

 =  = 8.

Hence, q = 2.

Answer.  q = 2.

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
    - Mathematical induction and geometric progressions
    - One characteristic property of geometric progressions
    - Solved problems on 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".

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