Question

There are 6 consecutive odd numbers in increasing order. the difference between the average of the squares of the first 4 numbers and the last 4 numbers is 64. if the sum of the squares of the first and the last element (i.e., odd numbers) is 178, then find the average of all the six numbers

Answer 1

Let 6nos. be x,x+2,x+4,x+6,x+8,x+10.
a. Sum of square of first and last element is 178.
x.x+x.x+100+20x=178
2x.x+20x-78=0
x.x+10x-39=0
(x+13)(x-3)=0
x=3,-13
When x=3
No's. are 3,5,7,9,11,13
Their avg. is 3+5+7+9+11+13/6
=48/6=8
When=-13
No's. are-13,-11,-9,-7,-5,-3
Their avg. is -13-11-9-7-5-3/6
=-48/6=-8
So avg of these no's.are(+-8).