SOLUTION: The sum of 128 consecutive odd, positive integers is the greatest power of two less than 200,000. The sum of the least and the greatest of these integers is 2^N. What is the value

Question 1168309: The sum of 128 consecutive odd, positive integers is the greatest power of two less than 200,000. The sum of the least and the greatest of these integers is 2^N. What is the value of N?
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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The sum of 128 consecutive odd, positive integers is the greatest power of two less than 200,000.
The sum of the least and the greatest of these integers is 2^N. What is the value of N?
~~~~~~~~~~~~~~~

 = 17.61 (approximately, with two decimals).


Therefore, the greatest power of 2 less than 200,000 is   = 131072.


So, the sum of 128 consecutive odd positive integers is  131072.


These consecutive integer numbers form an arithmetic progression;

therefore, their sum is the product of the number of terms (128) by half the sum of the least and the greatest of these two numbers.


In other words,   = .


It is equivalent to


     = ,  or

     = ,       or

     = .


It implies  17 = N + 6,  or  N = 17 - 6 = 11.


ANSWER.  N = 11.

Solved.

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