The sum of the first 100 odd numbers is divisible by: Options: A . &nbsp2, 4 and 8 B . &nbsp2 and 4 C . &nbsp2 only D . &nbspNone of these

The sum of the first 100 odd numbers is divisible by:

Question

The sum of the first 100 odd numbers is divisible by:

Options:

A . 2, 4 and 8

B . 2 and 4

C . 2 only

D . None of these

Answer: Option A
:
A
The sum of n consecutive odd numbers is given as

n^{2}

. Hence

100^{2}

is divisible by 2, 4 and 8. Answer is option (a).
(Sum of n consecutive odd numbers

= n^{2}

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

\times

2+1= 199. Therefore the sum =

\frac{(1 + 199) 100}{2} = 10000

n^{2}

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