Can anyone help me with this? I'm stuck again and don't 
understand this geometric sequence stuff. Any help would 
be appreciated!  Use the geometric sequence of numbers
1, 3, 9, 27, to find the following:

a). What is r, the ratio between 2 consecutive terms? 
Answer: 
Show work here: 

2nd term divided by 1st term = 3 ÷ 1 = 3
3rd term divided by 2nd term = 9 ÷ 3 = 3
4th term divided by 3rd term = 27 ÷ 9 = 3

Notice they all turned out to be 3.

That means that the common ratio, r, between terms, is 3.

That means that the rule for getting the next term
is to multiply by 3.  

1 times 3 is 3.
3 times 3 is 9.
9 times 3 is 27.

The next term not written is 81. That's because
27 times 3 is 81.

The next term after 81 that is not written is 243.
That's because 
81 times 3 is 243 
 
And so on and on.

------------------------------------

b) Using the formula for the nth term of a geometric 
sequence, what is the 10th term?

Answer: 
Show work here. 

The formula for the nth term of a geometric series is

an = a1rn-1 [Some books use t for a;
if yours uses t then replace all the a's by t's]

a10 = a1r10-1

a10 = a1r9

a1 stands for the first term, which is 1, and r stands for 
the ratio between terms, which we found to be 3.

a10 = 1(3)9

a10 = 19683

Checking
the 5th term is the 4th term times 3 which is 27 times 3 which is 81
the 6th term is the 5th term times 3 which is 81 times 3 which is 143
the 7th term is the 6th term times 3 which is 243 times 3 which is 729
the 8th term is the 7th term times 3 which is 729 times 3 which is 2187
the 9th term is the 8th term times 3 which is 2187 times 3 which is 6561
the 10th term is the 8rd term times 3 which is 6561 times 3 which is 19683

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c) Using the formula for the sum of a geometric sequence, 
what is the sum of the first 10 terms? 
Answer: 
Show work here 

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


        1(310 - 1)
S10 = ——————————————
           3 - 1 

        1(59049 - 1)
S10 = ——————————————
            2

       1(59048)
S10 = ——————————
           2

        59048
S10 = ————————
          2

S10 = 29524  

Checking: To check add up all the
terms found when we checked the (b) part.

               1
               3
               9
              27
              81
             243
             729
            2187
            6561
        +  19683
        --------
Total =    29524

Edwin