Question

Use the arithmetic sequence formula \(a_n=5+\left(n-1\right)\cdot2\) to complete the missing
values in the table.
x y
2
4

Answer 1

To complete the missing values in the table using the arithmetic sequence formula \(a_n = 5 + (n - 1) \cdot 2\), we first need to identify the values of \(n\) based on the provided \(x\) values.

Given:
- For \(x = 2\): \(n = 2\)
- For \(x = 4\): \(n = 4\)

Now, we can compute the corresponding \(y\) values:

1. **For \(n = 2\)**:
\[
a_2 = 5 + (2 - 1) \cdot 2 = 5 + 1 \cdot 2 = 5 + 2 = 7
\]

2. **For \(n = 4\)**:
\[
a_4 = 5 + (4 - 1) \cdot 2 = 5 + 3 \cdot 2 = 5 + 6 = 11
\]

Now we can fill the table:

\[
\begin{array}{c|c}
x & y \\
\hline
2 & 7 \\
4 & 11 \\
\end{array}
\]

Thus, the completed values are \(y = 7\) when \(x = 2\) and \(y = 11\) when \(x = 4\).