#### Answer

$d=-5t^2+q$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To find the common difference of the given arithmetic sequence,
\begin{array}{l}\require{cancel}
t^2+q, -4t^2+2q, -9t^2+3q,...
\end{array} subtract a term by its previous term.
$\bf{\text{Solution Details:}}$
Since the common difference of an arithmetic sequence is the difference between a term and its previous term, then with $a_2= -4t^2+2q $ and $a_1= t^2+q $, the common difference, $d$, is \begin{array}{l}\require{cancel}
d=a_2-a_1\\\\
d=-4t^2+2q-(t^2+q)
\\\\
d=-4t^2+2q-t^2-q
\\\\
d=(-4t^2-t^2)+(2q-q)
\\\\
d=-5t^2+q
.\end{array}