I am very frustrated. I am working on geometric series of numbers and thought
that it would be easy but, I have not done this in a while and I have to admit
that I am perplexed. Here is what I must solve: 
Use the geometric series of numbers 1, 2, 4, 8,...to find the following:
a) What is r, the ratio between 2 consecutive terms?
(I got r=1)

NO! First of all this is a SEQUENCE, not a SERIES. A SEQUENCE has commas
between its terms whereas a SERIES has plus signs between its terms.

There are three ways to find r for this geometric SEQUENCE.  DIVIDE any term
by the previous term.

First way to get r:

Divide the 2nd term by the 1st term. That is, 2 divided by 1 gives 2. So r=2

Second way to get r:

Divide the 3rd term by the 2nd term. That is, 4 divided by 2 gives 2. So r=2.

Third way to get r:

Divide the 4th term by the 3rd term. That is, 8 divided by 4 gives 2. So r=2. 

Now you know how to find the common ratio r.  I think you used SUBTRACTION,
which is what you use with an ARITHMETIC sequence to find the common
difference d, not common ratio r. You are getting a GEOMETRIC sequence
confused with an ARITHMETIC sequence.


b) Using the formula for the nth term of a geometric series, what it the 24th
term?

Again the word is SEQUENCE, not SERIES.  Use SEQUENCE when commas separate the
terms.  Use SERIES when plus (or minus) signs separate the terms.

The formula for the nth term of a geometric sequence is

an = a1rn-1

Here a1 = first term = 1, n = 24, r = 2

a24 = (1)(2)24-1

a24 = 223 = 8388608

 
c) Using the formula for the sum of a geometric series, what is the sum of the
first 10 terms? 

Now you are correctly asking about a SERIES 1 + 2 + 4 + 8 + ···

Sn = a1(rn-1)/(r-1)

n = 10, a1 = 1, r = 2

S10 = 1(210-1)/(2-1) = (210-1)/1 = 210-1 = 1024-1 = 1023

Edwin McCravy
AnlytcPhil@aol.com