設(shè)公比為q.
a1×a2×a3=(a2/q)×a2×(a2q)=a2³=1
a2=1
a4/a2=q²=(1/9)/1=1/9
q=1/3或q=-1/3
q=1/3時,
a1=a2/q=1/(1/3)=3
S5=a1(1-q^5)/(1-q)
=3×(1-1/3^5)/(1-1/3)
=(9/2)×(1-1/243)
=121/27
q=-1/3時,
a1=a2/q=1/(-1/3)=-3
S5=a1(1-q^5)/(1-q)
=(-3)×[1-(-1/3^5)]/[1-(-1/3)]
=(-9/4)×(1+1/243)
=(-9/4)×(244/243)
=-61/27
綜上,得：首項(xiàng)為3,公比為1/3,前5項(xiàng)和為121/27；或首項(xiàng)為-3,公比為-1/3,前5項(xiàng)和為-61/27.