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.
Algebra ->
Exponents
-> 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.
Log On
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):
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.
