Let me teach you some of the basics of a geometric series...

The difference between a sequence and a series is:

Series: $\displaystyle S_n = 1 + 2 + 4 + 8 + 16 + ... $

Sequence: $\displaystyle S_n = 1 ; 2 ; 4 ; 8 ; 16 ; ... $

A geometric series is formed by multiplying each term by a constant.

For example: $\displaystyle S_n = 1 + 2 + 4 + 8 + 16 + ... $

Could also be written as: $\displaystyle S_n = (1)(2^0) + (1)(2^1) + (1)(2^2) + (1)(2^3) + (1)(2^4) + ... $

The n-th term is equal to: $\displaystyle ar^{n - 1} $

$\displaystyle a $ is the starting term, the first term (a = 1 in the example).

$\displaystyle r $ is the common ratio (r = 2 in the example).

You can determine $\displaystyle r $ with the following formula: $\displaystyle r = \frac{T_2}{T_1} $

In series and sequences, the Sigma-sign is very important.

$\displaystyle \sum^{3}_{n = 0} (n + 1) = (0 + 1) + (1 + 1) + (2 + 1) + (3 + 1) = 10 $

Now i do hope that's all...