Question

the average of squares of 5 consecutive numbers is 18. What is the average of those numbers ?​

Answer 1

Hope you like my process

Given

5 consecutive numbers .

Let the third number be a

then the numbers would be

• a-2

• a-1

• a

• a+1

• a+2

Average of square of 5 numbers is 18

so total sum of square of 5 numbers are

= 18×5= 90

so ... By problem

=> (a-2)²+(a-1)²+a²+(a+1)²+(a+2)² =90

=> {(a+2)²+(a-2)²}+{(a-1)²+(a+1)²} + a² = 90

=> 2(a²+2²) +2(a²+1²)+a²=90

=> 2a² + 8 +2a² +2 + a²=90

=> 5a² = 90-10=80

=> a² = 80/5= 16

=> a = √16 = 4

so.......we got the value of a

Hence, the numbers are :

• a-2 = 4-2 = 2
• a-1 = 4-1 = 3
• a = 4+0 = 4
• a+1 = 4+1 = 5
• a+2 = 4+2 = 6

We got numbers , 2,3,4,5,6.

Thus the average is = (2+3+4+5+6)/5

= 20/5 = 4 answer.

--------------------

Hope this is your required answer

proud to help you ❤️