Question

which table represents an arithmetic sequence?

\

$$\begin{array}{|c|c|c|c|c|c|} \\hline n & 1 & 2 & 3 & 4 & 5 \\\\ \\hline a_n & -6 & -12 & -24 & -48 & -96 \\\\ \\hline \\end{array}$$

\

$$\begin{array}{|c|c|c|c|c|c|} \\hline n & 1 & 2 & 3 & 4 & 5 \\\\ \\hline a_n & 7 & 9 & 13 & 19 & 27 \\\\ \\hline \\end{array}$$

\

$$\begin{array}{|c|c|c|c|c|c|} \\hline n & 1 & 2 & 3 & 4 & 5 \\\\ \\hline a_n & 8.7 & 7.3 & 5.9 & 4.5 & 3.1 \\\\ \\hline \\end{array}$$

Explanation:

Define arithmetic sequence condition

Using the Arithmetic Sequences knowledge point
An arithmetic sequence has a constant difference \(d = a_{n} - a_{n-1}\) between consecutive terms.

Analyze the first table

Using the Arithmetic Sequences knowledge point

$$
LATEXBLOCK0
$$

Analyze the second table

Using the Arithmetic Sequences knowledge point

$$
LATEXBLOCK1
$$

Analyze the third table

Using the Arithmetic Sequences knowledge point

$$
LATEXBLOCK2
$$

Answer:

• (A) The table with values \(a_n = \{-6, -12, -24, -48, -96\}\)
• (B) The table with values \(a_n = \{7, 9, 13, 19, 27\}\)
• (C) The table with values \(a_n = \{8.7, 7.3, 5.9, 4.5, 3.1\}\) (Correct answer)