SOLUTION: Which of the following numbers can be expressed as a sum of 2 or more consecutive odd whole numbers?
i) 225 ii) 400
a) (i) only b) (ii) only c) Both (i) and (ii) d) none of t
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i) 225 ii) 400
a) (i) only b) (ii) only c) Both (i) and (ii) d) none of t
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Question 283356: Which of the following numbers can be expressed as a sum of 2 or more consecutive odd whole numbers?
i) 225 ii) 400
a) (i) only b) (ii) only c) Both (i) and (ii) d) none of these Found 2 solutions by nabla, richwmiller:Answer by nabla(475) (Show Source):
You can put this solution on YOUR website! Consider:
Odd numbers can be expressed as: 2k+1 (k a natural number)
Hence consecutive odds will be 2k+1 and 2k+3.
The sum of these two is 4k+4. Hence, the number must be even so case i is out.
4k+4=400 implies k=99.
So, 400 works. However, as per the tutor below there are additional cases to consider.
Now consider 3 odds.
2k+1,2k+3,2k+5. This gives 6k+9 as the sum. 6k+9=225 -> 6=16. So 225 fits the "or more" portion of the question. I hope this helps you see how to work the problem rather than just supplying the answer...
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