Question

09.
Prove that sum of two consecutive odd number is multiple of 4.​

Answer 1

$\huge \fbox{ \underline \purple{Answer }}$

Aim :

Let us Prove that sum of two consecutive odd number is multiple of  4

Let us Solve it by 2 methods

U can take any method which ever felt easy

METHOD 1 :

Let  

m  and  n  be two consecutive odd integers:

Sums of  m  and  n

3  +  5  =  8

5  +  7  =  12

7  +  9  =  16

From this result we can conclude 8 , 12, and 16 are the multiples of 4

METHOD 2 :

Consider:

( 2 n − 1 )  for any  n  ∈  Z  is an odd integer.  

The next consecutive odd integer will be  ( 2 n + 1 )

Sum  =  ( 2 n − 1 ) + ( 2 n + 1 )  = 4 n

Hence, the sum of any two consecutive odd integers will be a multiple of 4.

$\underline{\underline{ \sf \huge \red{✪Extra Bytes✪}}}$

Addition of two consecutive odd numbers are always multiples of 4 and also divisible by 4

Let us check some of those

✧ 3+ 5 = 8 and 8 is multiple and divisible by 4.

✧ 5 + 7 = 12 and 12 is multiple and divisible by 4.

✧ 7+ 9 = 16 and 16 is multiple and divisible by 4.

✧ 9 + 11 = 20 and 20 is multiple and  divisible by 4.