Question

consider the sequence:
6, 10, 14, 18, 22, ...

for this sequence, what is \\(a_3\\)?
\\(a_3 = 14\\)

which of the following describes the pattern in terms of the sequence?

• add 4 to the previous term to get the next term.
• add 6 to the previous term to get the next term.
• multiply the previous term by 3/5 to get the next term.
• multiply the previous term by 5/3 to get the next term.

Explanation:

Analyze the terms of the sequence

The given sequence is:

$$ 6, 10, 14, 18, 22, \dots $$

Calculate the differences between consecutive terms

$$
LATEXBLOCK0
$$

Identify the pattern

The difference between any term and its preceding term is a constant value of \(4\). Therefore, the pattern is to add \(4\) to the previous term to get the next term.

Answer:

• Add 4 to the previous term to get the next term. (Correct answer)
• Add 6 to the previous term to get the next term.
• Multiply the previous term by 3/5 to get the next term.
• Multiply the previous term by 5/3 to get the next term.