What is the value of the 34th term in the Fibonacci sequence?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. The sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth.

To find the 34th term, we would have to continue this pattern. However, this would be quite time-consuming.

Instead, we can use Binet's Formula, which is a closed-form expression that allows us to find the nth term in the Fibonacci sequence without having to find all the preceding terms.

Binet's Formula is as follows:

F(n) = (φ^n - (-φ^-n)) / √5

where φ = (1 + √5) / 2 (approximately 1.61803), which is the golden ratio, and n is the position in the Fibonacci sequence.

Let's plug in the values:

F(34) = ((1.61803^34) - (-1.61803^-34)) / √5

After calculating this expression, we find that the 34th term in the Fibonacci sequence is approximately 5702887.