Question 190367: # 4. Use inductive reasoning to determine the next three numbers in the pattern: 0, 1, 3, 6, 10, 15, ...
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! # 4
Q: Use inductive reasoning to determine the next three numbers in the pattern: 0, 1, 3, 6, 10, 15 ...
A:
Whenever you see a sequence of numbers, there is most often a relationship between the distance (or difference) of successive terms.
So if we take the first term 0 and subtract it from the second term 1, we get: 1-0=1
If we take the second term 1 and subtract it from the third term 3, we get: 3-1=2
If we take the third term 3 and subtract it from the fourth term 6, we get: 6-3=3 ... beginning to see a pattern?
If we take the fourth term 6 and subtract it from the fifth term 10, we get: 10-6=4
If we take the fifth term 10 and subtract it from the sixth term 15, we get: 15-10=5
So we found the differences to be: 1, 2, 3, 4, 5, ...
So as we move on, the differences increase by 1.
Using inductive reasoning, we would assume that this pattern continues indefinitely. So the next few differences should be 6, 7, 8, ...
So if we wanted to find the difference between the 6th and 7th term, that difference should be 6 (to stay consistent with the pattern)
Since the difference between the 6th and 7th term is 6, this means that we can add 6 to the 6th term 15 to get: 15+6=21
So the 7th term is 21
Continuing the pattern, the difference between the 7th and 8th terms is 7. So simply add 7 to 21 to get 21+7=28
So the 8th term is 28
Finally, the next difference is 8. Add 8 to 28 to get 28+8=36
So the 9th term is 36
So the next three numbers are 21, 28, and 36
Answer by solver91311(24713)  (Show Source):
|
|
|
