14. For a sequence specified by a recursive rule, finding an explicit expression for the th term is not easy, nor is the form necessarily simple. An exact expression for the th term of the Fibonacci sequence is given by the Binet formula:
Verify the formula for and by multiplying out, not by using a calculator.
Use the Binet formula and your calculator to find .
In fact, the second term on the right of the equation gets closer and closer to 0 as gets large. Because we know that the Fibonacci numbers are integers, we can just round off the result of calculating the first term. Find by calculating the first term with your calculator and rounding.