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# Geometric Sequences $t_n=a(r)^{n-1}$

1. 1
Given the sequence: $$3,\: 6,\: 12...$$
Find the 7th term.
2. 2
Given the sequence: $$1, -3,\; 9, -27...$$
Find the 8th term.
3. 3
Given the sequence: $$80,\: 40,\: 20...$$
Find $t_6$.
4. 4
Given the sequence: $$-729, \;243, -81...$$
Find $t_7$.
5. 5
How many terms are in the geometric sequence:
$$2,\: 6, \:18\,...\,1458$$
6. 6
How many terms are in the geometric sequence:
$$3, \,6, \,12\,...\,384$$
7. 7
How many terms are in the geometric sequence:
$$4, -2,\: 1\,...\,\frac{1}{64}$$
8. 8
Find a, r, and $t_n$ for the following geometric sequence. Then find $t_{8}$.
$$t_3={36}\, \quad t_{6}=972$$
9. 9
Find a, r, and $t_n$ for the following geometric sequence. Then find $t_{9}$.
$$t_4={12}\, \quad t_{6}=192$$
Good test question!
10. 10
Find a, r, and $t_n$ for the following geometric sequence. Then find $t_{8}$.
$$t_2={15} \, \quad t_{4}=135$$
11. 11
Find x so that the following are three terms of an geometric sequence.
$$x\, , \quad x+2\, , \quad x+3$$
12. 12
Find x so that the following are three terms of an geometric sequence.
$$x\, , \quad x+3\, , \quad 5x-3$$
Good test question!
13. 13
Find x so that the following are three terms of an geometric sequence.
$$2x\, , \quad x+5 \, , \quad x-7$$
14. 14
Find $t_7$ given:
$$\frac{2}{3}, \frac{5}{6}, \frac{8}{12}, \frac{11}{24}...$$
Good test question!

(You need to use both arithmetic and geometric formulas)

$$e=mc^2$$