Quadratics and Progressions

For constant $a$ , let the roots (of $x$ ) of the equation $x^2+ 2(a-3) x+9= 0$ lie between $-6$ and $1$ .

Given that

$2, h_1, h_2, h_3,\ldots,h_{20} , \lfloor a\rfloor$ follows a harmonic progression.
$2, a_1, a_2, a_3,\ldots,a_{20} , \lfloor a\rfloor$ follows an aritmetic progression.

Find the value of $a_3 \times h_{18}$ .