Insert 6 geometric means between 27 and 181.
Let G1,G2,G3,G4,G5,G6 be 6 geometric means between a=27 and b=181
Then, 27, G1,G2,G3,G4,G5,G6,181 is a G.P.
with common ratio r given by
r=(ba)1n+1
=(18127)16+1=(181×27)17=(137)17
∴G1=ar=27(13)=9
G2=ar2=27×19=3
G3=ar3=27×127=1
G4=ar4=27×127×3=13
G5=ar5=27×135=19
G6=ar6=27×136=127.
Hence, 9, 3, 1, 13,19,127 are 6 geometric means between 27 and 181.