SOLUTION: Determine the sum of the geometric sequence: 1 + 5 + 25 + ... + 3125.

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Question 1118014: Determine the sum of the geometric sequence: 1 + 5 + 25 + ... + 3125.
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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Geometric progression with the first term of 1 and the common ratio of 5.


The number of terms is 6:   5%5E%286-1%29 = 5%5E5 = 3125.


Use the formula for the sum of the first n terms of a Geom. progression with the first term a and the common ratio of r:


S%5Bn%5D = %28a%2Ar%5En+-+a%29%2F%28r-1%29.


Substitute the given values and calculate:


S%5B5%5D = 1%2A%285%5E6-1%29%2F%285-1%29 = 3906.

Solved.

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On geometric progressions,  see the introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
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 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.