Answer :

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]