What is the pattern to this sequence?
1,3,4,7,11,18,29
I figured it was plus the last 2 numbers which will then equal the next number. But I got messed up and can't figure the next 3 numbers in this pattern, any help is helpful.
THanks
You're right.
1 + 3 = 4
3 + 4 = 7
4 + 7 = 11
7 + 11 = 18
11 + 18 = 29
18 + 29 = ?
To find the pattern in the given sequence (1, 3, 4, 7, 11, 18, 29), let's examine the differences between consecutive terms:
3 - 1 = 2
4 - 3 = 1
7 - 4 = 3
11 - 7 = 4
18 - 11 = 7
29 - 18 = 11
The differences between consecutive terms are not constant, which means that the sequence does not follow a simple arithmetic pattern. However, we can still identify a pattern by considering the second differences:
1 - 2 = -1
3 - 1 = 2
4 - 3 = 1
7 - 4 = 3
11 - 7 = 4
The second differences are now constant (2), suggesting that the sequence may follow a quadratic or polynomial pattern.
To confirm this, let's calculate the third differences:
2 - (-1) = 3
1 - 2 = -1
3 - 1 = 2
4 - 3 = 1
The third differences are not constant, indicating that the sequence does not follow a cubic or higher-order polynomial pattern. Therefore, we can conclude that the sequence follows a quadratic pattern.
To find the next terms, we need to determine the quadratic formula that generates the sequence. We can assume that the formula is of the form: a * n^2 + b * n + c, where n represents the term number.
Now, let's substitute the first three terms of the sequence into the quadratic formula:
For n = 1: a + b + c = 1
For n = 2: 4a + 2b + c = 3
For n = 3: 9a + 3b + c = 4
Using these equations, we can solve for the values of a, b, and c. Once we have these values, we can continue the sequence by substituting higher values of n into the quadratic formula.
I will provide the calculations to solve for a, b, and c.