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Writing the Terms of a Geometric Sequence, write the first five terms of the geometric sequence. $$ a_{1}=4, r=-\frac{1}{\sqrt{2}} $$

Find the probability for the experiment of tossing a coin three times. Use the sample space \(S=H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T.\) The probability of getting at least two heads

Writing the Terms of a Sequence In Exercises \(7-22,\) write the first five terms of the sequence. (Assume that \(n\) begins with \(1 .\) ) $$ a_{n}=n\left(n^{2}-6\right) $$

True-False Exam In how many ways can you answer a 12 -question true-false exam? (Assume that you do not omit any questions.)

Finding the \(n\) th Term In Exercises \(21 - 30\) , find a formula for \(a _ { n }\) for the arithmetic sequence. $$ a _ { 1 } = 1 , d = 3 $$

Writing the Terms of a Sequence In Exercises \(7-22,\) write the first five terms of the sequence. (Assume that \(n\) begins with \(1 .\) ) $$ a_{n}=(-1)^{n}\left(\frac{n}{n+1}\right) $$

Using Mathematical Induction In Exercises \(11-24,\) use mathematical induction to prove the formula for every positive integer \(n .\) $$\sum_{i=1}^{n} i^{5}=\frac{n^{2}(n+1)^{2}\left(2 n^{2}+2 n-1\right)}{12}$$

License Plate Numbers In the state of Pennsylvania, each standard automobile license plate number consists of three letters followed by a four-digit number. How many distinct license plate numbers can be formed in Pennsylvania?

Find the probability for the experiment of drawing a card at random from a standard deck of 52 playing cards. The card is a face card.

Expanding an Expression In Exercises \(19-40,\) use the Binomial Theorem to expand and simplify the expression. $$(a+6)^{4}$$