Consecutive terms in this sequence are separated by a constant c, so if the 4th term is 15, then the next terms would be
5th: 15 + c
6th: (15 + c) + c = 15 + 2c
7th: (15 + 2c) + c = 15 + 3c
and so on. More generally, since any given number in the sequence depends on the number that came before it, we can write the n-th term in terms of the 4th term,
n-th: 15 + (n - 4) c
Then the 9th term in the sequence is
15 + (9 - 4) c = 35
and solving for c gives
15 + 5c = 35 ==> 5c = 20 ==> c = 4
Then the 15th term would be
15 + (15 - 4)×4 = 15 + 11×4 = 15 + 44 = 59
