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)

$$e=mc^2$$