13. Sequences, Series, and the Binomial Theorem

Geometric Sequences

Multiple Choice
Write the first four terms of the following geometric sequence.
$a_{1} = \frac{3}{4}, r = \frac{2}{3}$
Multiple Choice
Find the common ratio for the geometric sequence.
$0.8 comma 0.12 comma 0.018 comma 0.0027 comma dot dot dot$
Multiple Choice
Find the indicated term of the following geometric sequence.
$a_{n} = 4 (0.3)^{n - 1}$
Find $a sub 5$ .
Multiple Choice
Find the indicated term of the following geometric sequence.
$a_{n} = 10 (\frac{1}{5})^{n - 1}$
Find $a sub 4$
Multiple Choice
Identify if each sequence is arithmetic, geometric, or neither.
$7 comma 10 comma 16 comma 25 comma 37 comma dot dot dot$
Multiple Choice
Identify if each sequence is arithmetic, geometric, or neither.
$10 comma 5 comma five halves comma five fourths comma dot dot dot$
Multiple Choice
Write the first four terms of the following geometric sequence.
$a_{1} = - 8, r = - \frac{1}{2}$
Multiple Choice
Identify if each sequence is arithmetic, geometric, or neither.
$5 comma 11 comma 17 comma 23 comma 29 comma dot dot dot$
Multiple Choice
Write a formula for the general or $n^{t h}$ term for each geometric sequence.
$0.8 comma 0.32 comma 0.128 comma 0.0512 comma dot dot dot$
Multiple Choice
Find the common ratio for the geometric sequence.
$3 comma 12 comma 48 comma 192 comma dot dot dot$
Multiple Choice
Find the common ratio for the geometric sequence.
$6, - 3 \sqrt{2}, 3, - \frac{3 \sqrt{2}}{2}, \dots$
Multiple Choice
Find the common ratio for the geometric sequence.
$eighteen fifths comma six fifths comma two fifths comma 2 over 15 comma dot dot dot$
Multiple Choice
Write a formula for the general or $n^{t h}$ term for each geometric sequence.
$12, - 6, 3, - \frac{3}{2}, \dots$