Ardışık 17 tek sayının aritmetik ortalaması 21 dir bu sayılardan en büyüğü en küçüğünden kaç fazladır A)37 B)35 C)32 D)21 E)16
Cumaali said Ardışık 17 tek sayının aritmetik ortalaması 21 dir bu sayılardan en büyüğü en küçüğünden kaç fazladır A)37 B)35 C)32 D)21 E)16
Answer:
To solve this problem, follow these steps:

Understanding the Problem:
 We have 17 consecutive odd numbers.
 The arithmetic mean (average) of these 17 numbers is 21.
 We need to find the difference between the largest and smallest of these numbers.

Calculate the Sum of Numbers:

The arithmetic mean (average) of 17 numbers is given by:
\text{Average} = \frac{\text{Sum of numbers}}{\text{Number of terms}} 
Given, the average is 21 and the number of terms is 17:
21 = \frac{\text{Sum of numbers}}{17} 
Therefore, the sum of the numbers is:
\text{Sum of numbers} = 21 \times 17 = 357


Determine the Middle Term:

Since these numbers are consecutive odd numbers, the middle term (9th term) is the average:
\text{Middle term} = 21


Identify the Sequence:

With 21 as the middle term, we can deduce the sequence of odd numbers around this term:
 Middle term (9th term) is 21.
 The numbers before and after will be in steps of 2.

So the sequence is:
\{13, 15, 17, 19, 21, 23, 25, 27, 29\}


Find the Smallest and Largest Numbers:
 The smallest number (1st term) in this list is 13.
 The largest number (17th term) in this list is 29.

Calculate the Difference:

The difference between the largest and smallest numbers is:
29  13 = 16

Final Answer:
The difference between the largest and the smallest of these 17 consecutive odd numbers is \boxed{16}. Therefore, the correct option is E) 16.