Question

question 5 of 5

select the correct answer.

observe the sequences below.

i. \\(37, 41, 45, 49, \dots\\)
ii. \\(4, 24, 144, 864, \dots\\)
iii. \\(6, 12, 24, 48, \dots\\)
iv. \\(57, 63, 69, 75, \dots\\)

which sequence has a common difference of 6?

• i
• ii
• iii
• iv

Explanation:

⚡ Using what you learned: Arithmetic Sequences

Step 1: Analyze Sequence I

$$ 41 - 37 = 4 $$

$$ 45 - 41 = 4 $$

The common difference is \( 4 \).

Step 2: Analyze Sequence II

$$ \frac{24}{4} = 6 $$

$$ \frac{144}{24} = 6 $$

This is a geometric sequence with a common ratio of \( 6 \).

Step 3: Analyze Sequence III

$$ \frac{12}{6} = 2 $$

$$ \frac{24}{12} = 2 $$

This is a geometric sequence with a common ratio of \( 2 \).

Step 4: Analyze Sequence IV

$$ 63 - 57 = 6 $$

$$ 69 - 63 = 6 $$

$$ 75 - 69 = 6 $$

The common difference is \( 6 \).

Answer:

IV