There are altogether \(18\) numbers.

Let us assume the first number is \(x\) this leaves us with

17 numbers.

Since the numbers are consecutively odd such as

3,5,7 or 11,13,15.

Notice that for odd numbers there is a gap of

2 between successive numbers hence each number after the first will be 2 more than the previous number.

Hence the numbers will be such as

x,x+2,x+2+2,x+2+2+2....therefore if the first number is x the last number or the 18th number will be \(17*2 + x\)

since each number in the sequence are equally spaced the mean will be the avg of the first and last number.

which is \(\frac{x+x+38}{2} = \frac{2(x+17)}{2} = [m]x+17\)[/m]

From question \(x+17 = 534\)

therefore, \(x = 517\)

_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes