Question

which of the following represents a geometric sequence?

i \\(\frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \dots\\)

ii \\(\frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}, \dots\\)

iii \\(\frac{1}{4}, 1, -4, 16, \dots\\)

iv \\(\frac{1}{4}, -4, \frac{1}{4}, -4, \dots\\)

i
ii
iii
iv

Explanation:

Define geometric sequence condition

Using the Geometric Sequences and Common Ratio knowledge points

$$ r = \frac{a_{n+1}}{a_n} \quad \text{for all } n \ge 1 $$

Analyze sequence I

Using the Geometric Sequences and Common Ratio knowledge points

$$
LATEXBLOCK0
$$

Analyze sequence II

Using the Geometric Sequences and Common Ratio knowledge points

$$
LATEXBLOCK1
$$

Analyze sequence III

Using the Geometric Sequences and Common Ratio knowledge points

$$
LATEXBLOCK2
$$

Analyze sequence IV

Using the Geometric Sequences and Common Ratio knowledge points

$$
LATEXBLOCK3
$$

Answer:

• (A) I (Correct answer)
• (B) II
• (C) III
• (D) IV