Name: Introduction to Modulus Function Ix|
Uploaded: 2019-07-19
Duration: 2 min 28 s
Description: Absolute value means the magnitude of a real number without regard to its sign. Watch this video to learn about the absolute value function called the modulu...

Question

Show that one of three consecutive odd integers is a multiple of

3

.

Accepted Answer

Since it is an odd number

So $1^{s t}$ number be $2 n + 1$

Being consecutive odd

$2^{n d}$ number will be $2 n + 1 + 2 = 2 n + 3$ and $3^{r d}$ number $2 n + 5$ .

$2 n$ is always an even number and condition will revolve around this only giving rise to $2$ cases.

Case $1$ : if $2 n$ is divisible by $3$ then $2 n + 3$ will always be divisible by $3$ .

Case $2$ : if $2 n$ is not divisible by $3$ then remainder is either $1 or 2$ .

Now,

Case $2$ (a). Remainder $1$ implies $2 n - 1$ is divisible by $3$ .

If multiple of $3$ is added to $2 n - 1$ that will also be divisible by $3$ .

$= 2 n - 1 + 3 + 3$

$= 2 n - 1 + 2 \times 3$

$= 2 n + 5$

So $2 n + 5$ is divisible by $3$ .

Case $2$ (b) Remainder $2$ implies $2 n - 2$ is divisible by $3$ .

If multiple of $3$ is added to $2 n - 2$ that will also be divisible by $3$ .

$= 2 n - 2 + 3$

$= 2 n - 2 + 1 \times 3$

$= 2 n + 1$

So $2 n + 1$ is divisible by $3$ .

So from all the above case it is verified that out of $3$ consecutive odd number one will always be divisible by $3$ .

Show that one of three consecutive odd integers is a multiple of $3$ .

Important Questions on Number System

Learn and Prepare for any exam you want !

Show that one of three consecutive odd integers is a multiple of 3.

Important Questions on Number System

Learn and Prepare for any exam you want !

Show that one of three consecutive odd integers is a multiple of $3$ .