Final answer:
The next four terms in the given sequence are -5/9, 6/10, -7/11, and 8/12, continuing the pattern of alternating signs in numerators and incrementing denominators.
Step-by-step explanation:
Examining the sequence -1/5, 2/6, -3/7, 4/8, we can observe that there are clearly two alternating patterns: one for the numerators and one for the denominators. The numerators alternate in sign starting from -1 and increasing by 1 in absolute value each time (-1, 2, -3, 4). The denominators start at 5 and increase by 1 each time (5, 6, 7, 8).
Continuing this pattern, the next four terms in the sequence are calculated by following the established rules. The next numerator after 4 would be -5 (because we switch back to a negative) and the denominator would be 9 (incrementing by 1). Similarly, we'd proceed to 6/10, -7/11, and 8/12 for the subsequent terms.
Therefore, the next four terms in the sequence are -5/9, 6/10, -7/11, 8/12.