Let's solve the given problem step-by-step:
Given a list of numbers:
[tex]\[ 21, 1, -3, -10, 24 \][/tex]
We are asked to determine the values of `b` and `d`, and fill in the missing numbers accordingly.
- To find `b`, observe the difference between the 3rd and 2nd numbers:
[tex]\[ b = -3 - 1 = -4 \][/tex]
- For `d`, look at the difference between the 5th and 4th numbers:
[tex]\[ d = 24 - (-10) = 24 + 10 = 34 \][/tex]
- For `c`, no specific equation or difference is given other than `c = c`, which implies `c` is not defined in this context.
Now, filling in the missing values:
[tex]\[
\begin{array}{l}
21 \begin{array}{cccc}
1 & -3 & -10 & 24 \\
b & d \\
\end{array} \\
\begin{array}{cc}
1 & c \\
\end{array} \\
b = -4 \\
c = \, \text{not defined} \\
\end{array}
\][/tex]
Thus, the completed step is:
[tex]\[
\begin{array}{l}
21 \begin{array}{cccc}
1 & -3 & -10 & 24 \\
-4 & 34
\end{array} \\
\begin{array}{cc}
1 & \text{not defined}
\end{array} \\
b = -4 \\
c = c = \text{not defined}
\end{array}
\][/tex]
In summary:
[tex]\[
\boxed{
b = -4, \quad c = \text{not defined}, \quad d = 34
}
\][/tex]
