College Algebra, 4th Edition

Practice Test A

In Problems 1 and 2, write the first five terms of each sequence. State whether the sequence is arithmetic or geometric.

1. $a_n=3(5-4n)$

2. $a_n=-3(2^n)$

3. Write the first five terms of the sequence defined by $a_1=-2$ and $a_n=3a_{n-1}+5$ for $n\ge 2.$

4. Evaluate ${\displaystyle \frac{(n-1)!}{n!}}.$

5. Find $a_7$ for the arithmetic sequence with $a_1=-3$ and $d=4.$

6. Find $a_8$ for the geometric sequence with $a_1=13$ and $r=-{\displaystyle \frac{1}{2}}.$

In Problems 7–9, find each sum.

7. ${\displaystyle \sum _{k=1}^{20}(3k-2)}$

8. ${\displaystyle \sum _{k=1}^5\left({\displaystyle \frac{3}{4}}\right)(2^{-k})}$

9. ${\displaystyle \sum _{k=1}^{\infty }18{\left({\displaystyle \frac{1}{100}}\right)}^k};$ write the answer as a fraction in lowest terms.

10. Evaluate $\left(\begin{array}{c}13\\ 0\end{array}\right)$

11. Expand ${(1-2x)}^4.$

12. Find the term containing $x^1$ in the expansion of ${(2x+1)}^4.$

13. In how many ways can you answer every question on a ­ true–false test containing ten questions?

In Problems 14 and 15, evaluate each expression.

14. P(9, 2)

15. C(7, ...