Prove that the sum of two consecutive odd numbers is divisible by 4 – InterviewSolution

InterviewSolution

1.

Prove that the sum of two consecutive odd numbers is divisible by 4

Answer»

Let ( 2x + 1 ) , ( 2x + 3 ) are two

consecutive odd terms ,

Sum of two odd numbers

= 2x + 1 + 2x + 3

= 4x + 4

= 4 ( x + 1 )

= 4k ( let k = x + 1 )

4k is divisible by 4.

Therefore ,

Sum of any two consecutive odd

numbers divisible by 4 .

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