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:
Answer & explanation
Correct answer: option 3
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