Use inductive reasoning to predict the next three numbers in the sequence.
1, 0, -2, -5, -9,
1 - 1 = 0
0 - 2 = -2
-2 - 3 = -5
-5 - 4 = -9
What do you think will come next? What should be subtracted from -9?
1-1=0
0-2=-2
-2-3=-5
-5-4=-9
-9-5=-14 (would it be this)
Right. You're on the right track now to find the next two numbers.
predict the next three number in the pattern 12, 15, 18, 21, 24
To predict the next three numbers in the sequence using inductive reasoning, we need to observe the pattern or the relationship between the given numbers. Inductive reasoning involves looking for patterns and making assumptions based on those patterns.
Let's examine the differences between the consecutive terms in the sequence:
0 - 1 = -1
-2 - 0 = -2
-5 - (-2) = -3
-9 - (-5) = -4
The differences between each pair of consecutive terms are: -1, -2, -3, -4. From this information, we can infer that the differences are decreasing by one with each subsequent term.
Now let's continue this pattern to predict the next three numbers:
The difference between the current difference and the next difference is -1, so we get:
-4 - (-3) = -1
-1 - (-4) = 3
3 - (-1) = 4
Now, let's add these differences to the last number in the sequence, which is -9:
-9 + (-1) = -10
-9 + 3 = -6
-9 + 4 = -5
Therefore, using inductive reasoning, we can predict that the next three numbers in the sequence are -10, -6, -5.