Question
The sum of the first 100 odd numbers is divisible by:
Answer: Option A
:
A
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A
The sum of n consecutive odd numbers is given as n2 . Hence 1002 is divisible by 2, 4 and 8. Answer is option (a).
(Sum of n consecutive odd numbers =n2 is derived from unitary method as follows : 1 + 3 + 5 + 7 + 9 +...... is a series (AP) with a common difference of 2. Therefore, the 100th term would be 99×2+1= 199. Therefore the sum = (1+199)1002=10000 or n2.
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