Final answer:
The next two terms in the sequence using inductive reasoning are -13 and 35, based on a pattern of alternating signs and doubling changes.
Step-by-step explanation:
To find the next two terms of the sequence 5, -1, 11 using inductive reasoning, we first look for a pattern in the sequence given. Observing the sequence, we can see that the difference between successive terms is not constant, however, there seems to be an alternating pattern where the sign of the numbers changes from positive to negative and vice versa. The first term is positive, the second is negative, and the third is positive again. If this pattern continues, we would expect the fourth term to be negative.
If we look at the magnitudes of the numbers, they do not strictly increase or decrease. But noticing that 5 decreased to -1 (a change of -6), and then -1 increased to 11 (a change of +12), it seems there might be a pattern where the change is doubling each time but alternating in sign. Thus, the next change would be double 12 but negative, so -24. Applying this to 11 gives us 11 - 24 = -13.
Continuing this pattern, the subsequent change would be double 24 but positive, so +48. Applying this change to -13 gives -13 + 48 = 35.
Therefore, the next two terms in the sequence, based on this pattern of inductive reasoning, would be -13 and 35.