Question

( G cdot P: quad a, a r, a r^{2}, a r^{3} )
( a r^{2}=a+9 quad Rightarrow )
( Rightarrow aleft(r^{2}-1right)=9 )
( 8 quad a r=a r^{3}+18 Rightarrow a rleft(r^{2}-1right)=-18-Q )
Divide eq" O & ( frac{1}{gamma}=frac{-1}{2} Rightarrow r=-2 )
( Rightarrow quad 4 a=a+9 Rightarrow 3 a=9 Rightarrow a=3 )
( G P: quad 3,-6,12,-24 )

# (a) Find four numbers forming a geometric pro- gression in which the third term is greater than the first term by 9, and the second term is greater than the fourth by 18.

Solution