lean_workbook_plus_69720

The function that describes PigeonBoi420's behavior is described by the sequence $a_n=69+\sum_{i=1}^n{3i}$ . We then have the inequality $69+\frac{3n(n+1)}{2}>420$ . Simplifying, we get $3n^2+3n>702$ , so $n^2+n-234>0$ . Using the quadratic formula, our roots are $\frac{-1\pm\sqrt{937}}{2}$ We only care about the positive root, which evaluates to ~ $14.8052$ Therefore, PigeonBoi420 will haul in a number of pigeons greater than 420 in 15 days. So the answer is D.