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For low terms, it is probably most economical to to simply list out the sequence until you arrive at the nth term, but for large terms, there actually is a closed-form equation.

Let (phi) = (1 + sqrt(5))/2. As an aside, this is the golden ratio. Then the nth term of the Fibonacci sequence is given by

F(n) = [(phi)^n - (1 - (phi))^n]/sqrt(5),

where we are letting F(0) = 0, F(1) = 1, F(2) = 1, etc.

The derivation of this formula involves linear algebra, and, in short, the key is in setting this up as a matrix equation and diagonalizing the matrix. While I shall not run through the process here, I will give you the matrix and vector to start with:

Let A be the 2x2 matrix

[0 1]

[1 1]

and x(n) be the column vector in R^2

[F(n)]

[F(n+1)]

In particular, x(0) = (F(0),F(1)) = (0,1).

notice that [A][x(n)] =

[F(n+1)]

[F(n)+F(n+1)]

which is x(n+1). Thus, it follows that x(n) = [A]^n[x(0)] (you can prove this rigorously through induction). Now, F(n) is the first term of the vector x(n), so what one needs to do is diagonalize A, raise A to the appropriate power, multiply it with x(0), and finally take the upper term. The result is what I presented at the outset.

Note that with this formula you can show that lim(n-->infinity)[F(n+1)/F(n)] approaches phi.

Q: How do you calculate the nth term in the Fibonacci sequence?

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what? Assuming you wanted an algorithm to find the nth number in the Fibonacci sequence: double Fib(int i) { double x = 1; double y = 1; if (i

The sequence S = 2, 2, 4, 6, 10, 16, 26, ... is the Fibonacci sequence multiplied by 2. Like the Fibonacci sequence, each term is found by adding the two previous terms, so Sn = Sn-1 + Sn-2.

This is the Fibonacci sequence, where the number is the sum of the two preceding numbers. The nth term is the (n-1)th term added to (n-2)th term

By "the nth term" of a sequence we mean an expression that will allow us to calculate the term that is in the nth position of the sequence. For example consider the sequence 2, 4, 6, 8, 10,... The pattern is easy to see. # The first term is two. # The second term is two times two. # The third term is two times three. # The fourth term is two times four. # The tenth term is two times ten. # the nineteenth term is two times nineteen. # The nth term is two times n. In this sequence the nth term is 2n.

x(n)=x(n-1)+x(n-2) n, n-1 and n-1 are subscript.

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what? Assuming you wanted an algorithm to find the nth number in the Fibonacci sequence: double Fib(int i) { double x = 1; double y = 1; if (i

Good Question! After 6 years of math classes in college, and 30+ years of teaching (during which I took many summer classes) I've never seen an explicit formula for the nth term of the Fibonacci sequence. Study more math and maybe you can discover the explicit formula that you want.

The sequence S = 2, 2, 4, 6, 10, 16, 26, ... is the Fibonacci sequence multiplied by 2. Like the Fibonacci sequence, each term is found by adding the two previous terms, so Sn = Sn-1 + Sn-2.

The Fibonacci seuqnce is defined iteratively as follows: U1 = 1, U2 = 1 and Un = Un-2 + Un-1 for n>2

This is the Fibonacci sequence, where the number is the sum of the two preceding numbers. The nth term is the (n-1)th term added to (n-2)th term

123456789 * * * * * The nth term is 3n

By "the nth term" of a sequence we mean an expression that will allow us to calculate the term that is in the nth position of the sequence. For example consider the sequence 2, 4, 6, 8, 10,... The pattern is easy to see. # The first term is two. # The second term is two times two. # The third term is two times three. # The fourth term is two times four. # The tenth term is two times ten. # the nineteenth term is two times nineteen. # The nth term is two times n. In this sequence the nth term is 2n.

6n-5 is the nth term of this sequence

the first 4 terms of the sequence which has the nth term is a sequence of numbers that that goe together eg. 8,12,16,20,24 the nth term would be 4n+4

A single number, such as -3052 cannot define a sequence and, without a sequence you cannot have an nth term.

x(n)=x(n-1)+x(n-2) n, n-1 and n-1 are subscript.

The nth term is (36 - 4n)