Basic Technical Mathematics, 11th Edition

CHAPTER 19 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

1. For an arithmetic sequence, if $a_1\hspace{0.17em}=\hspace{0.17em}5\hspace{0.17em},\hspace{0.17em}d\hspace{0.17em}=\hspace{0.17em}3\hspace{0.17em},\hspace{0.17em}$ and $n\hspace{0.17em}=\hspace{0.17em}10\hspace{0.17em},\hspace{0.17em}$ then $a_{10}\hspace{0.17em}=\hspace{0.17em}35.$

2. For a geometric sequence, if $a_3\hspace{0.17em}=\hspace{0.17em}8\hspace{0.17em},\hspace{0.17em}{a}_5\hspace{0.17em}=\hspace{0.17em}2\hspace{0.17em},\hspace{0.17em}$ then $r\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{1}{2}}\hspace{0.17em}.\hspace{0.17em}$

3. The sum of the geometric series $6\hspace{0.17em}-\hspace{0.17em}2\hspace{0.17em}+\hspace{0.17em}{\displaystyle \frac{4}{3}}\hspace{0.17em}-\hspace{0.17em}\hspace{0.17em}\cdots \hspace{0.17em}\text{is }{\displaystyle \frac{9}{2}}\hspace{0.17em}.\hspace{0.17em}$

4. Evaluating the first three terms, ${(x\hspace{0.17em}+\hspace{0.17em}y)}^{10}\hspace{0.17em}=\hspace{0.17em}{x}^{10}\hspace{0.17em}+\hspace{0.17em}10x^{9}y\hspace{0.17em}+\hspace{0.17em}45x^8{y}^2\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}\cdots \hspace{0.17em}$

PRACTICE AND APPLICATIONS

In Exercises 5–12, find the indicated term of each sequence.

5. 1, 6, 11, … (17th)

6. $1\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}3\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}7\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}\dots \hspace{0.17em}$(21st)

7. 500, 100, 20, … (9th)

8. 0.025, 0.01, 0.004, … (7th)

9. $\hspace{0.17em}-\hspace{0.17em}1\hspace{0.17em},\hspace{0.17em}3.5\hspace{0.17em},\hspace{0.17em}8\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}\dots \hspace{0.17em}$(16th)

10. $\hspace{0.17em}-\hspace{0.17em}1\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{5}{3}}\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{7}{3}}\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}\dots \hspace{0.17em}$(25th)

11. ${\displaystyle \frac{3}{4}}\hspace{0.17em},\hspace{0.17em}{\displaystyle \frac{1}{2}}\hspace{0.17em},\hspace{0.17em}{\displaystyle \frac{1}{3}}\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}\dots \hspace{0.17em}$(7th)

12. $5^{\hspace{0.17em}-\hspace{0.17em}2}\hspace{0.17em},\hspace{0.17em}{5}^0\hspace{0.17em},\hspace{0.17em}{5}^2\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}\dots \hspace{0.17em}$(18th)

In Exercises 13–16, find the sum ...