Recursive Sequences:
find a formula for:
1,1,2,3,5,8,13,21
It looks like the Fibonacci sequence. Take the first two numbers and add them to get the 3rd. take the 2nd and third to get the fourth...etc.
yeah, but how would i write that into a formula?
What is the rule?
To find a formula for the given sequence, we can observe that each term is the sum of the two preceding terms in the sequence. This pattern is characteristic of the Fibonacci sequence.
Let's assume the formula for the nth term in the sequence is denoted as F(n).
We know that F(1) = 1 and F(2) = 1, which are the first two terms given in the sequence.
To calculate the third term, F(3), we add the previous two terms: F(1) + F(2) = 1 + 1 = 2.
Similarly, for the fourth term, F(4), we add the previous two terms: F(2) + F(3) = 1 + 2 = 3.
This pattern continues for the remaining terms in the sequence.
Based on this observation, we can write the formula for the recursive sequence as:
F(n) = F(n-1) + F(n-2)
This formula represents the recursive relationship between consecutive terms in the sequence.
To express the Fibonacci sequence as a formula, you can use a recursive approach. Let's denote the sequence as F(n), where n represents the position in the sequence. The formula for the Fibonacci sequence can be written as:
F(n) = F(n-1) + F(n-2)
where F(0) = 1 and F(1) = 1 are the initial terms. Using this formula, you can calculate any term in the Fibonacci sequence.