45 3rd term
135 4th term
405 5th term
1215 sixth term
This a geometric progression
Unknown at leading to equation
For this we need to know the at before knowing the a
Apply general formula
Tn=ar^n-1
T3=360=ar^3-1
360=ar^2.....................(1)
Also,
T6=1215=ar^6-1
1215=ar^5.....................(2)
Divide(2)by(1)
ar^5/ar^2 = 1215/45
By gradual reduction
a can cancel a in ar^5/ar^2
=r^5/r^2
Indices
r^5-2
r^3
1215/45= 27
Therefore, 27=r^3
3^3=r^3
Cube root both side to remove cube
r = 3
To get a the first term
Substitute r in equation 1 to get a
45=a(3)^2
45=a9
45=9a
Divide both side by 9
a=5