The average of squares of five consecutive odd natural numbers is 233. What is the average of the largest number and the smallest number?

15 

Let's assume numbers are x, x+2, x+4, x+6 & x+8

Sq. of the numbers will be x², (x+2)² ........ (x+8)²

As per question

5x² + (4 + 8 + 12 + 16)x + (2² + 4² + 6² + 8² ) = 233 x 5

5x² + 40x + 120 = 233 x5

x² + 8x + 24 = 233

x² + 8x - 209 = 0

x = 11 or -19

As all options are positive so x = 11

and last number of the series = 11 + 8 =19

The avg. of 1st and last number = 15