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Fill in the blanks. The coefficients of a binomial expansion are called ________ ________.

Fill in the blanks. The \( n \)th term of an arithmetic sequence has the form ________.

Fill in the blanks A sequence is an ________ sequence if the first differences are all the same nonzero number.

In Exercises 5 - 14, determine whether the sequence is arithmetic. If so, find the common difference. \( 4, 9, 14, 19, 24, \cdots \)

In Exercises 9 - 14, determine the sample space for the experiment. A coin and a six-sided die are tossed.

In Exercises 9 - 14, determine the sample space for the experiment. Two marbles are selected (without replacement) from a bag containing two red marbles, two blue marbles, and one yellow marble. The color of each marble is recorded.

In Exercises 15 - 20, find the probability for the experiment of tossing a coin three times. Use the sample space \( S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} \). The probability of getting exactly one tail

In Exercises 21 - 24, find the probability for the experiment of selecting one card from a standard deck of \( 52 \) playing cards. The card is not a face card.

How many three-digit numbers can be formed under each condition? (a) The leading digit cannot be zero. (b) The leading digit cannot be zero and no repetition of digits is allowed. (c) The leading digit cannot be zero and the number must be a multiple of \( 5 \). (d) The number is at least \( 400 \).

In Exercises 11 - 24, use mathematical induction to prove the formula for every positive integer \( n \). \( \sum_{i=1}^{n}i (i + 1) = \dfrac{n(n + 1)(n + 2)}{3} \)