1. Find the least number of terms that is required such that the geometric series 3 + 2 + 4/3 + … just exceeds 8.25. 2. The first term and common ratio of a geometric progression are a and r respectively. The geometric progression has 7 terms with the difference between the last term and the first term is 31 ½ , while the difference between the fourth term and the first term is 3 ½ . Find the sum of all the terms of the progression. ​

Our star pitcher, foster enlight, can throw a pitch so fast that it gets to the catcher’s mitt before it leaves foster’s fingers! if the team wins a game then the probability that foster was pitching is 0.8 but only if foster had at least one day’s rest since his last pitching assignment. if foster does not have a day off and the team still wins, the probability that foster was pitching drops by half of what it was on the previous day. if the team wins three games in succession from the toronto tachyons and foster pitched in game #2, what is the probability that he pitched in one or more of the other games? (assume that foster did not pitch on the day before the first game of this three game series.)