SOLUTION: The seventh term of a geometric sequence is twice the fifth term and the sum of the first seven terms is 254. All the terms are positive. Find the first term

Question 1083161: The seventh term of a geometric sequence is twice the fifth term and the sum of the first seven terms is 254. All the terms are positive. Find the first term
Answer by ikleyn(52802) (Show Source): You can put this solution on YOUR website!
.

Let "a" be the first term of the progression and "r" be the common ratio.

Then   =   and   =  .

Therefore,   =  = 2,  and,  hence,   = .


Then the sum is

254 =  = 


    =  = 


    =  = 


    = .


Hence,  a = .


Answer.  The first term is  a = .

Solved.

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

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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