Question

the average of 6consective even number is 11. find the greatest of the all 6 number​

Answer 1

Answer:

The required greatest number of all the 6 consecutive even numbers is 16

Step-by-step explanation:

Given :

The average of 6 consecutive even numbers is 11.

To find :

the greatest of all 6 numbers

Solution :

Let the 6 consecutive even numbers be

x , (x+2) , (x+4) , (x+6) , (x+8) and (x+10)

$\boxed{\sf Average=\dfrac{sum \ of \ observations}{number \ of \ observations}}$

The average of 6 consecutive even numbers is 11.

sum of the 6 consecutive even numbers/6 = 11

sum of the 6 consecutive even numbers = 11 × 6

sum of the 6 consecutive even numbers = 66

x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) = 66

   6x + 30 = 66

   6x = 66 - 30

   6x = 36

    x = 36/6

    x = 6

The consecutive even numbers are :

• x = 6
• x+2 = 6+2 = 8
• x+4 = 6+4 = 10
• x+6 = 6+6 = 12
• x+8 = 6+8 = 14
• x+10 = 6+10 = 16

The greatest of all the 6 consecutive even numbers is 16

$\rule{140}{1.5}$

Answer 2

$\sf{Answer}$

Step by step explanation:-

Given :-

Average of 6 consecutive even numbers = 11

To find :-

Greatest of all 6 numbers

Concept :-

Consecutive even numbers :-

Numbers which follow each other in order, without gaps, from smallest to largest. is called consecutive even numbers

Examples 2,4,6,8....

These are even numbers by consecutively difference is 2

Solution:-

As the above explanation

Similarly

Let the 6 consecutive even numbers are

• x
• x + 2
• x +4
• x + 6
• x + 8
• x + 10

Average = 11

We know that

$\sf{Average}$ = $\sf\dfrac{Sum\:of\:observations}{No\:of\:observations}$

So,

Sum of observations = x+(x+2)+(x+4)+x+6)+(x+8)+(x+10 )

Sum of observations = 6x + 30

No.of observations = 6

11 = $\sf\dfrac{6x+30}{6}$

66 = 6x + 30

66 - 30 = 6x

36 = 6x

x = 6

Finding numbers

• x = 6
• x +2 =8
• x + 4 = 10
• x + 6 = 12
• x + 8 = 14
• x +10 = 16

So, Required numbers are 6,8,10,12,14,16

Largest number is 16

Ur answer is 16

The greatest of all the 6 consecutive even numbers is 16