Answer Key 1

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Assuming the first term of each sequence is n=1:

1. $a_n=4-4n$ and $a_{20}=-76$
2. $a_n=\frac{2}{3}(n-1)$ and $a_{20}=\frac{38}{3}$
3. $a_n=36-11n$ and $a_{20}=-184$
4. $a_n=-5+\frac{7}{2}n$
5. $a_n=6–\frac{1}{2}n$
6. $a_n=-70+9n$
7. $a_n=-5+9n$
8. $a_n=22-4n$
9. $a_n=\frac{12}{5}–\frac{2}{5}n$
10. $2585$
11. $n=5$
12. $a_n=2\cdot 3^n$
13. $a_n=\frac{15}{2}\cdot {\left(\frac{2}{5}\right)}^n$
14. $a_n=8\cdot {\left(\frac{1}{2}\right)}^n$
15. $a_n=60\cdot {\left(\frac{1}{2}\right)}^n$
16. $a_n=-3072\cdot {(-\frac{1}{4})}^n$
17. $a_n=\frac{4}{5}\cdot 5^n$
18. $a_n=\frac{3}{2}\cdot 2^n$ or $a_n=\frac{3}{2}\cdot (-2{)}^n$
19. $a_n=-160\cdot 2^n$ or $a_n=-160\cdot (-2{)}^n$
20. $a_n=14\cdot {\left(\frac{1}{2}\right)}^n$ or $a_n=-14\cdot {(-\frac{1}{2})}^n$
21. $5115$ (Note, problem should read “…of the geometric series.”)

There’s also a chance that the teacher uses $(n-1)$ more than $n$ in the answers to 1-9 and 12-20. If so, then the teacher’s answers can be simplified into these answers.