The average of 5 consecutive odd numbers is 33. What is the product of the smallest and the largest of these five numbers?

Let's assume the smallest odd number of the given sequence is 'y'.

So 5 consecutive odd numbers are y, (y+2), (y+4), (y+6) and (y+8).

The average of 5 consecutive odd numbers is 33.

$$\frac{y+\left(y+2\right)+\left(y+4\right)+\left(y+6\right)+\left(y+8\right)}{5} = 33$$

$$\frac{5y+20}{5}=33$$

y+4 = 33

y = 33-4 = 29

Product of the smallest and the largest of these five numbers = y $$\times$$ (y+8)

= $$29\times(29+8)$$

= $$29\times37$$

= 1073