Mathematics - Sequence & Series Question with Solution | TestHub

Let $a_1,a_2,a_3,\dots$ be in an arithmetic progression of positive terms. Let ${\mathrm{A}}_{\mathrm{k}}={\mathrm{a}}_1^2-{\mathrm{a}}_2^2+{\mathrm{a}}_3^2-{\mathrm{a}}_4^2+\dots +{\mathrm{a}}_{2\mathrm{k}-1}^2-{\mathrm{a}}_{2\mathrm{k}}^2$. If ${\mathrm{A}}_3=-153,{\mathrm{A}}_5=-435$ and ${\mathrm{a}}_1^2+{\mathrm{a}}_2^2+{\mathrm{a}}_3^2=66$, then ${\mathrm{a}}_{17}-{\mathrm{A}}_7$ is equal to______