There are 5 consecutive odd numbers. If the difference between square of the average of first two odd number and the of the average last two odd numbers is 396, what is the smallest odd number?

Let the five consecutive odd numbers be x-4, x-2, x, x+2, x+4

According to the question,

Difference between square of the average of first two odd number and the of the average last

two odd numbers is 396

i.e, x+3 and x-3

$\Rightarrow x + 32 - x - 32 = 396\Rightarrow x2 + 9 + 6x - x2 + 6x - 9 = 396\Rightarrow 12x = 396\Rightarrow x = 33$

Hence, the smallest odd number is 33 - 4 = 29.