In the given progression, we have
`T_(2)/T_(1)={((sqrt(2)-1))/(2sqrt(3))xx1/1}=((sqrt(2)-1))/(2sqrt(3)), T_(3)/T_(2)=((3-2sqrt(2)))/12xx(2sqrt(3))/((sqrt(2)-1))=((sqrt(2)-1))/(2sqrt(3)), T_(4)/T_(3)=((5sqrt(2)-7))/(24sqrt(3))xx12/((3-2sqrt(2)))=((sqrt(2)-1))/(2sqrt(3))`.
`:. T_(2)/T_(1)=T_(3)/T_(2)=T_(4)/T_(3)=...=((sqrt(2)-1))/(2sqrt(3))` (costant).
So, the given progressionis a GP in which `a=1` and `r=((sqrt(2)-1))/(2sqrt(3))`.
`:.` the 5th term, `T_(5)=ar^((5-1))=ar^(4)=1xx((sqrt(2)-1)/(2sqrt(3)))^(4)`
`=((sqrt(2)-1)^(4))/144=((3-2sqrt(2))^(2))/144`
`=((17-12sqrt(2)))/144`
Hence, `T_(5)=((17-12sqrt(2)))/144`.
