How do you calculate the explicit formula and the nth term of the Fibonacci sequence?

(1/sq rt 5)((1+sq rt 5)/2)n - (1/sq rt 5)((1-sq rt 5)/2)n

This is based on the golden ratio (1+sq rt 5)/2) because the ratio of 2 Fibonacci terms approaches the golden ratio as the 2 terms used get larger. IE the ratio ot the 10th term to the 9th term is 55/34 = 1.61765 and the golden ratio is approx. 1.61803.

When using this formula if your calculator does not round, you will round to get the appropriate Fibonacci number.