Question

if Arithmetic mean of 9 consecutive integers is 35 then what is the difference between the third and the last integer? ​

Answer 1

To find : difference between the third and the last integer .

Given : arithmetic mean of $9$ consecutive integers is $35$ .

Solution :

• Average is the arithmetic mean.
• It is the ratio of sum of all the numbers given in data to the total number of observations.
• Formula: $Average =\frac{\text { sum of all the observations }}{\text { total of observations }}$
• Here, sum of observations :$= x + x +1 + x + 2+x +3 +x+4+x +5 +x +6 +x +7 +x +8$

        $= 9 x + 36 \\= 9 ( x + 4 )$

• Total number of observations $= 9$  
• average or arithmetic mean = $35$
• Substituting values in above formula,

       $35 = \frac{9 ( x + 4 )}{9} \\35 = x + 4 \\x = 35 -4 \\ x = 31$

• Hence , consecutive integers are : $31,32,33,34,35,36,37,38,39$
• Now , difference between the third and the last integer is :
• Third integer = $33$  and last integer = $39$

         $39 - 33 = 6$

Hence , difference between the third and the last integer is $6$ .

Answer 2

Answer:

Step-by-step explanation: