a1, a2, a3 geometry progression
24/a1 , 60/a2 , 126/a3 arithmetic
the first 3 terms sum in geometric is 38 and the common ratio or quotient is less than 2
You need a second equation to get a system of equations.
$\dfrac{126}{ar^2}-\dfrac{60}{ar}=\dfrac{60}{ar}-\dfrac{24}{a}$
Multiply out by $ar^2$ to get:
$126-60r=60r-24r^2$
$4r^2-20r+21=0$
$(4r-7)(r-3)=0$
Because the ratio is less than 2, this leaves only one solution. Plug that into the equation Plato showed you and solve for $a$.