Chapter 1: Sequences and Series

Objectives:

1. Derive a rule for determining the sum of n terms of a geometric series.
   
2. Determine the first term, the common ratio, the number of terms, or the value of the sum of a specific number of terms in a problem involving a geometric series.

A Geometric Series is the expression for the sum of terms of a Geometric Sequence.

Again, the common ratio and general term will be the same for the corresponding sequence. 

The sum of a Geometric Sequence can be shown to be 

S_n =\( \frac{t_1(r^n - 1)}{r - 1} \), \( r \neq 1 \) and S_n = \( \frac{t_1r^n - t_1}{r - 1} \), \( r \neq 1 \)

Example:

For the Geometric Series 4 + 8 + 16 + 32 + 64 + ...

S₈ = \( \frac{4(2^8 - 1)}{1} \) = 4(255) 1020