Learning Materials
Features
Discover
Chapter 5: Problem 92
Use the order of operations to find the value of each expression. \(5(-3)^{2}-2(-2)^{3}\)
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
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 \(2019 .\)
The sum, \(S_{n}\), of the first n terms of an arithmetic sequence is given by $$ S_{n}=\frac{n}{2}\left(a_{1}+a_{n}\right), $$ in which \(a_{1}\) is the first term and \(a_{n}\) is the nth term. The sum, \(S_{n}\), of the first \(n\) terms of a geometric sequence is given by $$ S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}, $$ in which \(a_{1}\) is the first term and \(r\) is the common ratio \((r \neq 1)\). Determine whether each sequence is arithmetic or geometric. Then use the appropriate formula to find \(S_{10}\), the sum of the first ten terms. \(3,-6,12,-24, \ldots\)
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. \(6,1,-4,-9, \ldots\)
Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0004,-0.004,0.04,-0.4, \ldots\)
Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\frac{2}{3}, 1, \frac{4}{3}, \frac{5}{3}, \ldots\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine