Given a quadratic pattern 4 p 11 q 22 which has a constant difference of 1 .show tha p=7 and q=16

Question

Quadratic pattern :4;p;11;q;22 which have a constant difference of 1

Show that P= 7 and Q=16

Answer 1

\begin{aligned}
&1^{\text {st }} \text { difference } \\
&p-4 ; 11-p ; q-11 ; 22-q \\
&2^{\text {nd }} \text { difference} \\
&-2 p+15 ; q+p-22 ; 33-2 q \\
&-2 p+15=1 \\
&-2 p=-14 \\
&p=7 \\
&\begin{array}{rl}
33-2 q=1 & q+p-22=1 \\
-2 q=-32 & \text { or/of }
\end{array} \quad q+7-22=1 \\
&q=16 & q=16
\end{aligned}