SOLUTION: The sum of 36 consecutive odd, positive integers is the greatest perfect cube less than 50 000. Find the sum of the least and the greatest of the integers.

Question 1099659: The sum of 36 consecutive odd, positive integers is the greatest perfect cube less than 50 000. Find the sum of the least and the greatest of the integers.
Answer by ikleyn(52925) (Show Source): You can put this solution on YOUR website!
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The cube root of 50000 is  = 36.84  (approximately).


Hence, the perfect cube the condition says about, is  = 46656.


Thus the sum of the given progression is equal to this number 46656.


This sum is the sum of the first and the last terms of the AP taken  = 18 times.


    (This fact must be clear to anyone who studied arithmetic progressions).


So, the sum under the question is   = 2592.

Answer. The sum under the question is 2592.

Solved.

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There is a bunch of lessons on arithmetic progressions in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic 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 "Arithmetic 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.

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