Question

There are 4 geometric mean between 3 and 729. Find the

sum of the G.P.

Answer 1

write the geometric series

$3, 3r, 3r^2, 3r^3, 3r^4, 729$

where r is the common ratio

$3r^5=729$

$r^5=243$

$r=243^{1/5}=3$

sum of G.P=$3+3r+3r^2+3r^3+3r^4+729=3+3(3)+3(3)^2+3(3)^3+3(3)^4+729=1092$