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(52787)   (Show Source):
You can put this solution on YOUR website! .
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?
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 = 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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