Question

the first four terms of a geometric sequence are 108, 36, 12, 4, ...
what is the common ratio?
-72
-3
3
\\(\frac{1}{3}\\)

the fish population in a lake decreases by 2% each year.
what is the common ratio?
-0.02
-0.98
0.02
0.98

Explanation:

Calculate the common ratio of the sequence

Using the Common Ratio and Geometric Sequences knowledge points

$$ r = \frac{a_2}{a_1} = \frac{36}{108} = \frac{1}{3} $$

Determine the common ratio for the population decay

Using the Exponential Decay Modeling knowledge point

$$
LATEXBLOCK0
$$

Answer:

Question 1

• (A) \(-72\)
• (B) \(-3\)
• (C) \(3\)
• (D) \(\frac{1}{3}\) (Correct answer)

Question 2

• (A) \(-0.02\)
• (B) \(-0.98\)
• (C) \(0.02\)
• (D) \(0.98\) (Correct answer)