Question

x y
2 a
4 b

Use the arithmetic sequence formula An=-8+(n-1)*2 to find the missing values in the table

Answer 1

To fill in the missing values in the table using the arithmetic sequence formula \( A_n = -8 + (n-1) \cdot 2 \), we will first determine the values of \( A_n \) for each \( n \) corresponding to the \( x \) values in the table.

Given the table:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & a \\
4 & b \\
\hline
\end{array}
\]

Now, we will find \( A_2 \) and \( A_4 \):

1. For \( n = 2 \):
\[
A_2 = -8 + (2 - 1) \cdot 2 = -8 + 1 \cdot 2 = -8 + 2 = -6
\]
Thus, \( a = -6 \).

2. For \( n = 4 \):
\[
A_4 = -8 + (4 - 1) \cdot 2 = -8 + 3 \cdot 2 = -8 + 6 = -2
\]
Thus, \( b = -2 \).

The completed table is:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & -6 \\
4 & -2 \\
\hline
\end{array}
\]