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The arithmetic mean of 10 consecutive even integers is 3. What is the least of these 10 even integers?

 Jul 1, 2019
 #1
avatar+625 
+4

The arithmetic mean of 10 consecutive even integers is 3. What is the least of these 10 even integers? If the mean is 3, then five of the numbers must be less than 3 and five greater than 3. The numbers less than 3 must be −6, −4, −2, 0, 2 and those greater than 3 must be 4, 6, 8, 10, and 12. The least of these is −6 .

 

-tommarvoloriddle

 Jul 2, 2019
edited by tommarvoloriddle  Jul 2, 2019
 #2
avatar+101813 
+2

THX, tommarvoloriddle   !!!

 

Here's one other way

 

Let 2n be the smallest integer  and  2n + 18  the largest

 

The sum of these  divided by 2 will = the mean

 

So

 

[ 2n + 2n + 18 ]

____________   =     3            multiply both sides by 2

         2

 

2n + 2n +18  =  6

 

4n + 18  =  6          subtract  18 from both sides

 

4n  =  -12   divide both sides by 4

 

n =  - 3  

 

So...the smallest integer  = 2n  = 2(-3)  = - 6

 

 

cool cool cool

 Jul 2, 2019
 #3
avatar+625 
+3

Wow.. That was better Phrased... Not my Question, But Thank You!

tommarvoloriddle  Jul 2, 2019

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