Look over the following sequence of numbers. What are the next 3 numbers in the pattern?what is the pattern rule?
-1,0,1,0,1,2,3,6,11,20,37
This is (probably) a series with a recurrence relation:
a(n)=a(n-3)+a(n-2)+a(n-1)
Try
0=-1+0+1
1=0+1+0
2=1+0+1
...
37=6+11+20
Some call this tribonacci numbers, from
Fibonacci numbers where
a(n)=a(n-2)+a(n-1)
Thanks so much
How do get the three numbers relative I understand that the number u get is the first to add for the next in the pattern?
Are the three numbers 63. 89. 115???????
Basically, you add the three last numbers to get the next, for example,
2+3+6=11, ...
So the next number is:
11+20+37 = 68
20+37+68 = ?
...
To identify the pattern rule in a sequence of numbers and find the next elements, we usually need to analyze the sequence and look for any recurring patterns or relationships between the numbers.
Looking at the given sequence: -1, 0, 1, 0, 1, 2, 3, 6, 11, 20, 37
We observe that the numbers seem to switch between incrementing and decrementing. Let's break down the sequence and identify the pattern:
Step 1: Starting from -1, we see an increment of 1 in the next number, resulting in 0.
Step 2: The next number decreases by 1, resulting in -1.
Step 3: Now, the pattern seems to repeat with an increment of 1, resulting in 0 again.
Step 4: The next number decreases by 1, resulting in -1.
So, we have identified the repeating pattern of incrementing and decrementing values: 1, -1, 1, -1.
Now, to find the next three numbers in the pattern, we continue this same pattern:
Step 5: Incrementing by 1 from -1, we get 0.
Step 6: The next number will be -1 since we continue with the decrementing pattern.
Step 7: Incrementing by 1 from -1, we get 0 again.
Therefore, the next three numbers in the pattern are: 0, -1, 0.
Hence, the pattern rule for the given sequence is an alternating pattern of incrementing by 1 and decrementing by 1.