Course: College Algebra
Topic: Sequences and Series
Subtopic: Geometric Sequences and Series


Our studies today take us into the second of two special sequences. Sequences such as `5, 10, 20, 40, 80, ...` where you multiply a fixed number to get the next terms are called geometric sequences. This particular sequence can be written in general as `{5*2^n-1}`. Again it is important to be able to write the first few terms given this general formula or derive it when given the sequence's terms. Geometric series are sums where the terms are geometric such as `5+10+20+40+80+....`

Something to think about: Some infinite geometric series have finite sums. Under what conditions do infinite geometric series have finite sums?


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: geometric sequence, first term, common ratio, nth term, geometric series, geometric sequence & series formulae

Text Notes

Concentrate on the algebraic techniques, particularly finding the n-th term, number of terms, and sum. Pay attention to the differences between a finite and infinite geometric sum.