Find the next three values in the following sequence of numbers.
-1,0,1,0,1,2,3,6,11,20,37
-1,0,1,0,1,2,3,6,11,20,37,68,125,230,423,778...
A new number is obtained by adding the 3 previous ones.
To find the next three values in the given sequence of numbers, we can try to identify a pattern or rule that governs the sequence. Let's analyze the differences between consecutive terms:
-1, 0, 1, 0, 1, 2, 3, 6, 11, 20, 37
The differences between consecutive terms are:
(0 - (-1)) = 1
(1 - 0) = 1
(0 - 1) = -1
(1 - 0) = 1
(2 - 1) = 1
(3 - 2) = 1
(6 - 3) = 3
(11 - 6) = 5
(20 - 11) = 9
(37 - 20) = 17
The differences between consecutive terms seem to be increasing by 2 each time. Let's test this pattern by applying it to continue the sequence:
The next difference would be (17 + 2) = 19.
To find the next term, we add the last difference (19) to the last term (37):
37 + 19 = 56. So, the next term is 56.
The next difference would be (19 + 2) = 21.
To find the term after that, we add the last difference (21) to the last term (56):
56 + 21 = 77. So, the term after 56 is 77.
The next difference would be (21 + 2) = 23.
To find the term after that, we add the last difference (23) to the last term (77):
77 + 23 = 100. So, the term after 77 is 100.
Therefore, the next three values in the sequence are 56, 77, and 100.