Since the sequence is evenly spaced, we know that the mean=median=mean of first and last term.
Let x = first term.
Since there are 18 terms in the sequence, and the sequence is made up of odd consecutive terms, we know that the last term can be represented as x + 2*17 = x + 34.
mean = mean of first and last term gives us:
534 = (x + x +34)/2
534 = x + 17
x = 534 - 17
x = 517
Another approach is that since there are 18 terms, the median is equal to the average of the two middle terms (terms 9 and 10), denote these two terms T9, T10.
534 = mean = median = T9+T10/2.
Since T9 and T10 are consecutive integers, T9 = 533 and T10 = 535.
Since the terms are consecutive, odd integers, keep subtracting 2 to get back to T1.
T9 = 533
T8 = 531
T7 = 529
T6 = 527
T5 = 525
T4 = 523
T3 = 521
T2 = 519
T1 = 517
This second approach might seem longer, but it may be more intuitive. Using your first approach, you must make sure that you figure out what the last term is in terms of the first term (initial thought might be x + 36).
If you aren't comfortable making these moves with evenly spaced number sets, then check out Manhattan GMAT's Number Properties book.
