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Chapter 8: Problem 8
Write the first five terms of each geometric sequence. $$a_{n}=-6 a_{n-1}, \quad a_{1}=-2$$
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Will help you prepare for the material covered in the next section. Consider the sequence \(8,3,-2,-7,-12, \ldots .\) Find \(a_{2}-a_{1}\) \(a_{3}-a_{2}, a_{4}-a_{3},\) and \(a_{5}-a_{4}\). What do you observe?
Use the formula for \(_{n} C_{r}\) to solve A four-person committee is to be elected from an organization's membership of 11 people. How many different committees are possible?
Some three-digit numbers, such as 101 and \(313,\) read the same forward and backward. If you select a number from all three digit numbers, find the probability that it will read the same forward and backward.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I modeled California's population growth with a geometric sequence, so my model is an exponential function whose domain is the set of natural numbers.
The president of a large company with \(10,000\) employees is considering mandatory cocaine testing for every employee. The test that would be used is \(90 \%\) accurate, meaning that it will detect \(90 \%\) of the cocaine users who are tested, and that \(90 \%\) of the nonusers will test negative. This also means that the test gives \(10 \%\) false positive. Suppose that \(1 \%\) of the employees actually use cocaine. Find the probability that someone who tests positive for cocaine use is, indeed, a user.
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