## College Algebra (11th Edition)

$d=-5t^2+q$
$\bf{\text{Solution Outline:}}$ 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}