The average of the squares of four consecutive odd natural numbers is 201. The average of 7 times of the largest number and 3 times of the smallest number is:

76

Sum of the squares of four consecutive odd natural numbers is = 4 × 201 = 804

Let smallest odd number is = a

a2 + ( a+2)² + (a+4)2 + (a+6)2 = 804

a2 + a2 + 4 + 4a + a2 + 16 + 8a + a2 + 36 + 12a = 804

4a2 + 24a + 56 = 804

a2 + 6a + 8 = 201

On solving ,

a = 11

Smallest number  = 11 & largest number = 17

Required average = \(\frac{ 7 × 17 + 3 × 11 }{2}\) 

= \(\frac{ 152 }{2}\) = 76