The sequence LXIV (64), XXXVI (36), XVI (16) follows the pattern of halving each term: 64, 36 (half of 72), 16 (half of 32). The pattern is actually squares being halved: 8²=64, 6²=36, 4²=16, so the next term is 2²=4, which is IV in Roman numerals. Option II (2) would be too small, while IX (9) and X (10) don't fit the pattern.