+0  
 
-1
99
1
avatar+229 

The arithmetic mean of an odd number of consecutive odd integers is $y$. Find the sum of the smallest and largest of the integers in terms of $y$. 

 Feb 20, 2021
 #1
avatar+118069 
+1

Let's  use  a couple of  examples  and  see if  we  can generate an answer

 

Let one  series be

 

1, 3, 5 , 7 , 9

 

The  mean is     [ 1 + 3  +  5 + 7 + 9 ]  /  5  =  25 /  5  =  5  =  y

 

Sum of largest and smallest values =   10  =  2y

 

Let  another  series  be

 

11, 13,  15, 17, 19

 

The mean  is    15

 

So....it  appears that  the mean  =   the   median value

 

Sum of largest and smallest value =   30   =  2y

 

So...... it appears  that  the  sum of the  largest  and smallest  value  =  2 * average  =    2y

 

 

cool cool cool

 Feb 20, 2021

30 Online Users

avatar
avatar