The quadratic formula gives the solutions for a quadratic equation of the form . Solutions to this equation are given by the following formula:
Consider the sequence generated by the recursion rule
a. Find the first 12 numbers in this sequence.
b. Find the ratios of consecutive pairs of numbers in the sequence 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 ratios you found in part (b). What do you notice?
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