A geometric series has the general formula for calculating the next number as follows
Series is 5, 15 , 45 , T4 , T5 , T6
Next Term (or nth term) = ar^n-1
a = first term, i.e. 5
r = common ratio i.e. 3 (as 15/5=3 and 45/15=3 so this must be a common ratio all through)
n = the next terms we're to calculate....
as you already have 1st , 2nd and 3rd terms..then the next one is 4th then 5th and 6th.
therefore n= 4
substituting now
T4= ar^n-1
= 5*3^4-1
= 5*3^3
= 5*27
T4 = 135
T5= ar^n-1
= 5*3^5-1
= 5*3^4
= 5*81
T5 = 405
T6= ar^n-1
= 5*3^6-1
= 5*3^5
= 5*243
T6= 1215
Therefore whole series is 5, 15, 45, 135, 405, 1215 withe the last 3 being your required ones.
