what is a geometric series?
http://en.wikipedia.org/wiki/Geometric_progression (this is a web site if you want to take a look)
Now,
3,6,12,24,48
43046721, 14348907, 4782969, 1594323,
27, 3, 1, 1/3, 1/9, 1/27
2,-6,18,-54
are all examples of GPs (geometric progressions)
Geometric Series are geometric progressions with + signs inbetween each term.
GPs have a first term referred to as 'a' or 'a 1' and a common ratio referred to as r
so the first term is 'a' (same as T 1)
the second term T 2 is a*r = ar
the third term T 3 is the second *r = ar*r = ar 2
the forth term T 4 is the third *r = ar 2*r = ar 3
the nth term called T n or (sometimes a n depending on what country you are studyinging in) and you can substitute in any value for n is
T n= ar (n-1)
I don't know how good your algebra is but in the examples above can you find 'a' and 'r' of each one? There is a formula to do this but if you think hard you might not need the formula.
I hope you find this interesting.
+118654 
