Let ak = 4k + 4 and bk = (k − 1)3 + 3k + 5 for every integer k ≥ 0. What are the first five terms defined by ak? a0 = a1 = a2 = a3 = a4 = What are the first five terms defined by bk? b0 = b1 = b2 = b3 = b4 = Do the first five terms of these two sequences have any terms in common? Yes. Only the first term in both sequences are identical. Yes. Only the first two terms in both sequences are identical. Yes. Only the first three terms in both sequences are identical. Yes. Only the first four terms in both sequences are identical. Yes. The first five terms of both sequences are identical. No. These two sequences have no terms in common.

Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)