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Chapter 5: Problem 53
Perform the indicated operation. Simplify the answer when possible. \(\frac{1}{4} \sqrt{12}-\frac{1}{2} \sqrt{48}\)
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Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{40}\), when \(a_{1}=6, r=-1\).
Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=-3\)
Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,-21,-35, \ldots\)
The bar graph shows changes in the percentage of college graduates for Americans ages 25 and older from 1990 to 2010. Exercises 125-126 involve developing arithmetic sequences that model the data. In \(1990,24.4 \%\) of American men ages 25 and older had graduated from college. On average, this percentage has increased by approximately \(0.3\) each year. a. Write a formula for the \(n\)th term of the arithmetic sequence that models the percentage of American men ages 25 and older who had graduated from college \(n\) years after \(1989 .\) b. Use the model from part (a) to project the percentage of American men ages 25 and older who will be college graduates by \(2019 .\)
Write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20 th term of the sequence. \(a_{1}=9, d=2\)
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