The quadratic formula gives the solutions for a quadratic equation of the form . Solutio...

The quadratic formula gives the solutions for a quadratic equation of the form . Solutions to this equation are given by the following formula:

Pell numbers are generated by the recursion rule

a. Find the first 12 Pell numbers.

b. Find the ratios of consecutive pairs of Pell numbers from part (a); that is, calculate What do you notice about the ratios?

c. Use the quadratic formula to find solutions to the quadratic equation and compare your answers to the quotients from part (b). What do you notice?